Straight Lines and Pair of Straight Lines PYQs - Last 5 Years
JEE Main / Mathematics / Coordinate Geometry / 85 recent questions
MathematicsCoordinate Geometry2022-2026
Practice 85 JEE Main Mathematics questions from Straight Lines and Pair of Straight Lines. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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Last 5 Years Straight Lines and Pair of Straight Lines Questions
Showing 50 of 85 filtered questions.
1Straight Lines And Pair Of Straight Lines
If a straight line drawn through the point of intersection of the lines $4 x+3 y-1=0$ and $3 x+4 y-1=0$, meets the co-ordinate axes at the points P and Q , then the locus of the mid point of PQ is :
MCQ+4 / -12026
2Straight Lines And Pair Of Straight Lines
In an equilateral triangle $P Q R$, let the vertex $P$ be at $(3,5)$ and the side $Q R$ be along the line $x+y=4$. If the orthocentre of the triangle PQR is $(\alpha, \beta)$, then $9(\alpha+\beta)$ is equal to:
MCQ+4 / -12026
3Straight Lines And Pair Of Straight Lines
From the point $(-1,-1)$, two rays are sent making angles of $45^{\circ}$ with the line $x+y=0$. These rays get reflected from the mirror $x+2 y=1$. If the equations of the reflected rays are $\mathrm{a} x+\mathrm{b} y=9$ and $c x+d y=7, a,...
INTEGER+4 / -12026
4Straight Lines And Pair Of Straight Lines
Let the vertex A of a triangle ABC be $(1,2)$, and the mid-point of the side AB be $(5,-1)$. If the centroid of this triangle is $(3,4)$ and its circumcenter is $(\alpha, \beta)$, then $21(\alpha+\beta)$ is equal to :
MCQ+4 / -12026
5Straight Lines And Pair Of Straight Lines
Let the line $\mathrm{L}_1: x+3=0$ intersect the lines $\mathrm{L}_2: x-y=0$ and $\mathrm{L}_3: 3 x+y=0$ at the points A and B , respectively. Let the bisector of the obtuse angle between the lines $L_2$ and $L_3$ intersect the line $L_1$ a...
MCQ+4 / -12026
6Straight Lines And Pair Of Straight Lines
Let $\mathrm{A}, \mathrm{B}$ be points on the two half-lines $x-\sqrt{3}|y|=\alpha, \alpha>0$ at a distance of $\alpha$ from their point of intersection $P$. The line segment $A B$ meets the angle bisector of the given half-lines at the poi...
INTEGER+4 / -12026
7Straight Lines And Pair Of Straight Lines
Let the mid points of the sides of a triangle ABC be $\left(\frac{5}{2}, 7\right)$, $\left(\frac{5}{2}, 3\right)$ and $(4, 5)$. If its incentre is $(h, k)$, then $3h + k$ is equal to :
MCQ+4 / -12026
8Straight Lines And Pair Of Straight Lines
Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line $x+2 \sqrt{2} y=4$. If the co-ordinates of the vertex A are $(\alpha, \beta)$, then the greatest integer less than or equal to $|\alpha+\sqrt{2} \...
MCQ+4 / -12026
9Straight Lines And Pair Of Straight Lines
Let $A(1,0), B(2,-1)$ and $C\left(\frac{7}{3}, \frac{4}{3}\right)$ be three points. If the equation of the bisector of the angle ABC is $\alpha x+\beta y=5$, then the value of $\alpha^2+\beta^2$ is
MCQ+4 / -12026
10Straight Lines And Pair Of Straight Lines
Let the angles made with the positive $x$-axis by two straight lines drawn from the point $\mathrm{P}(2,3)$ and meeting the line $x+y=6$ at a distance $\sqrt{\frac{2}{3}}$ from the point P be $\theta_1$ and $\theta_2$. Then the value of $\l...
MCQ+4 / -12026
11Straight Lines And Pair Of Straight Lines
A rectangle is formed by the lines $x=0, y=0, x=3$ and $y=4$. Let the line L be perpendicular to $3 x+y+6=0$ and divide the area of the rectangle into two equal parts. Then the distance of the point $\left(\frac{1}{2},-5\right)$ from the li...
MCQ+4 / -12026
12Straight Lines And Pair Of Straight Lines
Let $\mathrm{A}(1,2)$ and $\mathrm{C}(-3,-6)$ be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to the line $7 x-y=14$. If $\mathrm{B}(\alpha, \beta)$ and $\mathrm{D}(\gamma, \delta)$ are the other two ver...
MCQ+4 / -12026
13Straight Lines And Pair Of Straight Lines
Among the statements
$(S 1)$ : If $A(5,-1)$ and $B(-2,3)$ are two vertices of a triangle, whose orthocentre is $(0,0)$, then its third vertex is $(-4,-7)$
and
(S2) : If positive numbers $2 a, b, c$ are three consecutive terms of an A.P., th...
$(S 1)$ : If $A(5,-1)$ and $B(-2,3)$ are two vertices of a triangle, whose orthocentre is $(0,0)$, then its third vertex is $(-4,-7)$
and
(S2) : If positive numbers $2 a, b, c$ are three consecutive terms of an A.P., th...
MCQ+4 / -12026
14Straight Lines And Pair Of Straight Lines
Let a point A lie between the parallel lines $\mathrm{L}_1$ and $\mathrm{L}_2$ such that its distances from $\mathrm{L}_1$ and $\mathrm{L}_2$ are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle ABC , wh...
MCQ+4 / -12026
15Straight Lines And Pair Of Straight Lines
A line passing through the point P($a$, 0) makes an acute angle \(\alpha\) with the positive x-axis. Let this line be rotated about the point P through an angle $\frac{\alpha}{2}$ in the clockwise direction. If in the new position, the slo...
MCQ+4 / -12025
16Straight Lines And Pair Of Straight Lines
Let a be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle \(\alpha\) with the positive x-axis and the equations of its diagonals are $(\sqrt{3}+1)x+(\sqrt{3}-1)y=0$ and $(\sqrt{3}-1)x-(\sqrt{3...
MCQ+4 / -12025
17Straight Lines And Pair Of Straight Lines
Let ABC be the triangle such that the equations of lines AB and AC be $3 y-x=2$ and $x+y=2$, respectively, and the points B and C lie on $x$-axis. If P is the orthocentre of the triangle ABC , then the area of the triangle PBC is equal to
MCQ+4 / -12025
18Straight Lines And Pair Of Straight Lines
If the orthocenter of the triangle formed by the lines y = x + 1, y = 4x - 8 and y = mx + c is at (3, -1), then m - c is :
MCQ+4 / -12025
19Straight Lines And Pair Of Straight Lines
Let the three sides of a triangle are on the lines $4 x-7 y+10=0, x+y=5$ and $7 x+4 y=15$. Then the distance of its orthocentre from the orthocentre of the tringle formed by the lines $x=0, y=0$ and $x+y=1$ is
MCQ+4 / -12025
20Straight Lines And Pair Of Straight Lines
A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $\mathrm{L}_1: 2 x+y+6=0$ and $\mathrm{L}_2: 4 x+2 y-p=0, p>0$, at the points A and B , respectively. If $A B=\frac{9}{\sqrt{...
MCQ+4 / -12025
21Straight Lines And Pair Of Straight Lines
Consider the lines $x(3 \lambda+1)+y(7 \lambda+2)=17 \lambda+5, \lambda$ being a parameter, all passing through a point P. One of these lines (say $L$ ) is farthest from the origin. If the distance of $L$ from the point $(3,6)$ is $d$, then...
MCQ+4 / -12025
22Straight Lines And Pair Of Straight Lines
Let the area of the triangle formed by a straight line $\mathrm{L}: x+\mathrm{b} y+\mathrm{c}=0$ with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line L makes an angle of $45^{\circ}$ with the posi...
MCQ+4 / -12025
23Straight Lines And Pair Of Straight Lines
Let ΔABC be a triangle formed by the lines 7x – 6y + 3 = 0, x + 2y – 31 = 0 and 9x – 2y – 19 = 0. Let the point (h, k) be the image of the centroid of ΔABC in the line 3x + 6y – 53 = 0. Then h2 + k2 + hk is equal to :
MCQ+4 / -12025
24Straight Lines And Pair Of Straight Lines
Let the line x + y = 1 meet the axes of x and y at A and B, respectively. A right angled triangle AMN is inscribed in the triangle OAB, where O is the origin and the points M and N lie on the lines OB and AB, respectively. If the area of th...
MCQ+4 / -12025
25Straight Lines And Pair Of Straight Lines
If A and B are the points of intersection of the circle $x^2 + y^2 - 8x = 0$ and the hyperbola $\frac{x^2}{9} - \frac{y^2}{4} = 1$ and a point P moves on the line $2x - 3y + 4 = 0$, then the centroid of $\Delta PAB$ lies on the line :
MCQ+4 / -12025
26Straight Lines And Pair Of Straight Lines
Two equal sides of an isosceles triangle are along $ -x + 2y = 4 $ and $ x + y = 4 $. If $ m $ is the slope of its third side, then the sum, of all possible distinct values of $ m $, is:
MCQ+4 / -12025
27Straight Lines And Pair Of Straight Lines
Let the lines $3 x-4 y-\alpha=0,8 x-11 y-33=0$, and $2 x-3 y+\lambda=0$ be concurrent. If the image of the point
$(1,2)$ in the line $2 x-3 y+\lambda=0$ is $\left(\frac{57}{13}, \frac{-40}{13}\right)$, then $|\alpha \lambda|$ is equal to
$(1,2)$ in the line $2 x-3 y+\lambda=0$ is $\left(\frac{57}{13}, \frac{-40}{13}\right)$, then $|\alpha \lambda|$ is equal to
MCQ+4 / -12025
28Straight Lines And Pair Of Straight Lines
Let the points $\left(\frac{11}{2}, \alpha\right)$ lie on or inside the triangle with sides $x+y=11, x+2 y=16$ and $2 x+3 y=29$. Then the product of the smallest and the largest values of $\alpha$ is equal to :
MCQ+4 / -12025
29Straight Lines And Pair Of Straight Lines
A rod of length eight units moves such that its ends $A$ and $B$ always lie on the lines $x-y+2=0$ and $y+2=0$, respectively. If the locus of the point $P$, that divides the rod $A B$ internally in the ratio $2: 1$ is $9\left(x^2+\alpha y^2...
MCQ+4 / -12025
30Straight Lines And Pair Of Straight Lines
Let the triangle PQR be the image of the triangle with vertices $(1,3),(3,1)$ and $(2,4)$ in the line $x+2 y=2$. If the centroid of $\triangle \mathrm{PQR}$ is the point $(\alpha, \beta)$, then $15(\alpha-\beta)$ is equal to :
MCQ+4 / -12025
31Straight Lines And Pair Of Straight Lines
Let the distance between two parallel lines be 5 units and a point $P$ lie between the lines at a unit distance from one of them. An equilateral triangle $P Q R$ is formed such that $Q$ lies on one of the parallel lines, while R lies on the...
INTEGER+4 / -12025
32Straight Lines And Pair Of Straight Lines
A ray of light coming from the point \(\mathrm{P}(1,2)\) gets reflected from the point \(\mathrm{Q}\) on the \(x\)-axis and then passes through the point \(R(4,3)\). If the point \(S(h, k)\) is such that \(P Q R S\) is a parallelogram, then...
MCQ+4 / -12024
33Straight Lines And Pair Of Straight Lines
A variable line \(\mathrm{L}\) passes through the point \((3,5)\) and intersects the positive coordinate axes at the points \(\mathrm{A}\) and \(\mathrm{B}\). The minimum area of the triangle \(\mathrm{OAB}\), where \(\mathrm{O}\) is the or...
MCQ+4 / -12024
34Straight Lines And Pair Of Straight Lines
The equations of two sides \(\mathrm{AB}\) and \(\mathrm{AC}\) of a triangle \(\mathrm{ABC}\) are \(4 x+y=14\) and \(3 x-2 y=5\), respectively. The point \(\left(2,-\frac{4}{3}\right)\) divides the third side \(\mathrm{BC}\) internally in t...
MCQ+4 / -12024
35Straight Lines And Pair Of Straight Lines
If the orthocentre of the triangle formed by the lines \(2 x+3 y-1=0, x+2 y-1=0\) and \(a x+b y-1=0\), is the centroid of another triangle, whose circumcentre and orthocentre respectively are \((3,4)\) and \((-6,-8)\), then the value of $$|...
INTEGER+4 / -12024
36Straight Lines And Pair Of Straight Lines
Let a ray of light passing through the point \((3,10)\) reflects on the line \(2 x+y=6\) and the reflected ray passes through the point \((7,2)\). If the equation of the incident ray is \(a x+b y+1=0\), then \(a^2+b^2+3 a b\) is equal to __...
INTEGER+4 / -12024
37Straight Lines And Pair Of Straight Lines
If the line segment joining the points \((5,2)\) and \((2, a)\) subtends an angle \(\frac{\pi}{4}\) at the origin, then the absolute value of the product of all possible values of $a$ is :
MCQ+4 / -12024
38Straight Lines And Pair Of Straight Lines
Let a variable line of slope \(m>0\) passing through the point \((4,-9)\) intersect the coordinate axes at the points \(A\) and \(B\). The minimum value of the sum of the distances of \(A\) and \(B\) from the origin is
MCQ+4 / -12024
39Straight Lines And Pair Of Straight Lines
If the locus of the point, whose distances from the point \((2,1)\) and \((1,3)\) are in the ratio \(5: 4\), is \(a x^2+b y^2+c x y+d x+e y+170=0\), then the value of \(a^2+2 b+3 c+4 d+e\) is equal to :
MCQ+4 / -12024
40Straight Lines And Pair Of Straight Lines
Let two straight lines drawn from the origin \(\mathrm{O}\) intersect the line \(3 x+4 y=12\) at the points \(\mathrm{P}\) and \(\mathrm{Q}\) such that \(\triangle \mathrm{OPQ}\) is an isosceles triangle and $$\angle \mathrm{POQ}=90^{\circ}...
MCQ+4 / -12024
41Straight Lines And Pair Of Straight Lines
Let \(\mathrm{A}(-1,1)\) and \(\mathrm{B}(2,3)\) be two points and \(\mathrm{P}\) be a variable point above the line \(\mathrm{AB}\) such that the area of \(\triangle \mathrm{PAB}\) is 10. If the locus of \(\mathrm{P}\) is $$\mathrm{a} x+\m...
MCQ+4 / -12024
42Straight Lines And Pair Of Straight Lines
The vertices of a triangle are \(\mathrm{A}(-1,3), \mathrm{B}(-2,2)\) and \(\mathrm{C}(3,-1)\). A new triangle is formed by shifting the sides of the triangle by one unit inwards. Then the equation of the side of the new triangle nearest to...
MCQ+4 / -12024
43Straight Lines And Pair Of Straight Lines
Let \(\alpha, \beta, \gamma, \delta \in \mathbb{Z}\) and let \(A(\alpha, \beta), B(1,0), C(\gamma, \delta)\) and \(D(1,2)\) be the vertices of a parallelogram \(\mathrm{ABCD}\). If \(A B=\sqrt{10}\) and the points \(\mathrm{A}\) and $$\math...
MCQ+4 / -12024
44Straight Lines And Pair Of Straight Lines
Let \(A(-2,-1), B(1,0), C(\alpha, \beta)\) and \(D(\gamma, \delta)\) be the vertices of a parallelogram \(A B C D\). If the point \(C\) lies on \(2 x-y=5\) and the point \(D\) lies on \(3 x-2 y=6\), then the value of $$|\alpha+\beta+\gamma+...
INTEGER+4 / -12024
45Straight Lines And Pair Of Straight Lines
Let \(A(a, b), B(3,4)\) and \(C(-6,-8)\) respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point \(P(2 a+3,7 b+5)\) from the line \(2 x+3 y-4=0\) measured parallel to the line $$x-2 y-1=...
MCQ+4 / -12024
46Straight Lines And Pair Of Straight Lines
A line passing through the point \(\mathrm{A}(9,0)\) makes an angle of \(30^{\circ}\) with the positive direction of \(x\)-axis. If this line is rotated about A through an angle of \(15^{\circ}\) in the clockwise direction, then its equatio...
MCQ+4 / -12024
47Straight Lines And Pair Of Straight Lines
If \(x^2-y^2+2 h x y+2 g x+2 f y+c=0\) is the locus of a point, which moves such that it is always equidistant from the lines \(x+2 y+7=0\) and \(2 x-y+8=0\), then the value of \(g+c+h-f\) equals
MCQ+4 / -12024
48Straight Lines And Pair Of Straight Lines
In a \(\triangle A B C\), suppose \(y=x\) is the equation of the bisector of the angle \(B\) and the equation of the side \(A C\) is \(2 x-y=2\). If \(2 A B=B C\) and the points \(A\) and \(B\) are respectively \((4,6)\) and $$(\alpha, \bet...
MCQ+4 / -12024
49Straight Lines And Pair Of Straight Lines
The distance of the point \((2,3)\) from the line \(2 x-3 y+28=0\), measured parallel to the line \(\sqrt{3} x-y+1=0\), is equal to
MCQ+4 / -12024
50Straight Lines And Pair Of Straight Lines
Let \(\mathrm{A}\) be the point of intersection of the lines \(3 x+2 y=14,5 x-y=6\) and \(\mathrm{B}\) be the point of intersection of the lines \(4 x+3 y=8,6 x+y=5\). The distance of the point \(P(5,-2)\) from the line \(\mathrm{AB}\) is
MCQ+4 / -12024