Straight Lines and Pair of Straight Lines PYQs - Last 5 Years
MHT CET / Mathematics / Coordinate Geometry / 126 recent questions
MathematicsCoordinate Geometry2022-2026
Practice 126 MHT CET 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 126 filtered questions.
1Straight Lines And Pair Of Straight Lines
If the equation $16x^2 - 24xy + 9y^2 - 8x + 6y - 35 = 0$ represents a pair of straight lines, then the equation of the locus of points equidistant from these two lines is..........
MCQ+2 / -02026
2Straight Lines And Pair Of Straight Lines
The area of a triangle formed by a line with the coordinate axes is $49$ sq. units. If the perpendicular drawn from the origin to this line makes an angle of $45^\circ$ with the positive X-axis, then the equation of line is....
MCQ+2 / -02026
3Straight Lines And Pair Of Straight Lines
If the angle made by the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ with X-axis are $\alpha$ and $\beta$, then $\tan(\alpha + \beta)$ is
MCQ+2 / -02026
4Straight Lines And Pair Of Straight Lines
A straight line makes equal negative intercepts on the coordinate axes. If the perpendicular distance from the origin to the line is 4 units, then the equation of the line is ......
MCQ+2 / -02026
5Straight Lines And Pair Of Straight Lines
If the combined equation of angle bisectors of the lines $x^2 - 2pxy - y^2 = 0$ is $x^2 - 2qxy - y^2 = 0$, then which of the following is true?
MCQ+2 / -02026
6Straight Lines And Pair Of Straight Lines
A straight line L passes through the point of intersection of the lines $x - y + 1 = 0$ and $2x + y - 7 = 0$. If L intersects the positive x-axis at $A(a, 0)$ and the positive y-axis at $B(0, b)$, then the minimum area of the triangle $OAB$...
MCQ+2 / -02026
7Straight Lines And Pair Of Straight Lines
If two lines represented by $x^2 - (1 + \sqrt{3})xy + \sqrt{3}y^2 = 0$ make angles $\alpha$ and $\beta$ with the X-axis, then $\tan(\alpha + \beta)$ is...
MCQ+2 / -02026
8Straight Lines And Pair Of Straight Lines
The family of straight lines $4ax + 3by + c = 0$ such that $a + b + c = 0$ (where a, b, c are real constants) are concurrent at the point...
MCQ+2 / -02026
9Straight Lines And Pair Of Straight Lines
Two lines are given by $x^2 - 4xy + 4y^2 + kx - 2ky = 0$, then the value of k so that the distance between them is 3 is
MCQ+2 / -02026
10Straight Lines And Pair Of Straight Lines
The line $L_1$ given by $\dfrac{x}{p} + \dfrac{y}{2} = 1$ passes through the point $(5,0)$. The line $L_2$ given by $\dfrac{x}{10} + \dfrac{y}{q} = 1$ is parallel to $L_1$. Then the distance between the lines $L_1$ and $L_2$ is...
MCQ+2 / -02026
11Straight Lines And Pair Of Straight Lines
The combined equation of lines parallel to the coordinate axes and passing through the point of intersection of lines represented by $x^2 - 6xy + 5y^2 + 10x - 14y + 9 = 0$ is $\ldots$
MCQ+2 / -02026
12Straight Lines And Pair Of Straight Lines
The coordinates of the orthocenter of the triangle whose sides are represented by the lines $4x - 7y + 10 = 0$, $x + y = 5$ and $7x + 4y = 15$ are $\ldots$
MCQ+2 / -02026
13Straight Lines And Pair Of Straight Lines
The joint equation of a pair of lines passing through point $(1,4)$, one of which is parallel to X-axis and the other makes an angle of $45^\circ$ with the positive direction of X-axis, is
MCQ+2 / -02026
14Straight Lines And Pair Of Straight Lines
The measure of the acute angle between the pair of lines $2x^2 + xy - y^2 - x + 2y - 1 = 0$ is:
MCQ+2 / -02026
15Straight Lines And Pair Of Straight Lines
If $A(2, -3)$ and $C(-6, 7)$ are opposite vertices of a rhombus ABCD, then the equation of diagonal BD is
MCQ+2 / -02026
16Straight Lines And Pair Of Straight Lines
If the equation $ax^2 + 4xy - 2y^2 + 4x + 8y + 1 = 0$ represents a pair of straight lines, then the coordinates of their point of intersection are.........
MCQ+2 / -02026
17Straight Lines And Pair Of Straight Lines
The line $y = 2x + c$ passes through a point that is equidistant from both the axes and lies in the first quadrant $(x > 0, y > 0)$. Then the value of c is...
MCQ+2 / -02026
18Straight Lines And Pair Of Straight Lines
A triangle has two fixed vertices A $(a, 0)$ and B$(0, b)$ . Let its third vertex C is moving along the line $x = y$. If $s$ is the area of triangle ABC, then $\dfrac{ds}{dx} =$
MCQ+2 / -02026
19Straight Lines And Pair Of Straight Lines
If $4ab = 3h^2$, then the ratio of the slopes of the lines represented by $ax^2 + 2hxy + by^2 = 0$ is...
MCQ+2 / -02026
20Straight Lines And Pair Of Straight Lines
The number of lines passing through A (3, 4) and the sum of whose non-zero intercepts is zero is (are)
MCQ+2 / -02026
21Straight Lines And Pair Of Straight Lines
The combined equation of the pair of lines passing through the origin and making an angle $\dfrac{\pi}{4}$ with the line $3x + y - 6 = 0$ is...
MCQ+2 / -02026
22Straight Lines And Pair Of Straight Lines
If $\theta$ is the acute angle between the lines $2x^2 + 7xy + 3y^2 = 0$, then the value of $\dfrac{2\cos\theta - 3\sin\theta}{4\sin\theta + 5\cos\theta} = \ldots$
MCQ+2 / -02026
23Straight Lines And Pair Of Straight Lines
The line $(2 + k)x + (1 + k)y = 5 + 7k$ passes through the fixed point for different values of k. If 'd' is the distance of a fixed point from the origin, then $d^2 = \ldots$
MCQ+2 / -02026
24Straight Lines And Pair Of Straight Lines
The triangle formed by the lines $2x^2 - 3xy - 2y^2 = 0$ and $3x - y = 7$ is...
MCQ+2 / -02026
25Straight Lines And Pair Of Straight Lines
If $\theta$ is the acute angle between the lines represented by the equation $x^2 - 3xy + 2y^2 = 0$, then $\dfrac{3\sin\theta + 2\cos\theta}{3\sin\theta - 2\cos\theta} = $
MCQ+2 / -02026
26Straight Lines And Pair Of Straight Lines
If a triangle $ABC$ has vertices $A(1,-6), B(2,-3)$ and $C(3,-2)$, then the coordinates of its orthocenter are....
MCQ+2 / -02026
27Straight Lines And Pair Of Straight Lines
The line $x + y = 3$ intersects the pair of straight lines $x^2 - 3xy + y^2 = 0$ at points A and B. Then the co-ordinates of the mid-point of AB are
MCQ+2 / -02026
28Straight Lines And Pair Of Straight Lines
The equation of the line passing through the point of intersection of the lines $x + 2y + 6 = 0$ and $2x - y = 2$ and making an intercept 5 on the y-axis is
MCQ+2 / -02026
29Straight Lines And Pair Of Straight Lines
The joint equation of the pair of lines through the origin and making an angle of $\dfrac{\pi}{4}$ with the line $3x + y - 6 = 0$ is
MCQ+2 / -02026
30Straight Lines And Pair Of Straight Lines
The area of the triangle formed by the co-ordinate axes and a line $px + qy = r$ (where p, q and r are positive real numbers) is $\dfrac{1}{54}$ sq.units, then ....
MCQ+2 / -02026
31Straight Lines And Pair Of Straight Lines
The pair of straight lines represented by the equation $\sqrt{3}x^2 - 4xy + \sqrt{3}y^2 = 0$ are
MCQ+2 / -02026
32Straight Lines And Pair Of Straight Lines
If the equation $kx^2 - 5xy + 6y^2 + x - 3y = 0$ represents a pair of straight lines, then the co-ordinates of their point of intersection are
MCQ+2 / -02026
33Straight Lines And Pair Of Straight Lines
The equation of the straight line passing through the point $(-5, 3)$ such that the portion of the line intercepted between the axes is divided by the point in the ratio $4:3$ (from the X-axis to the Y-axis) is...
MCQ+2 / -02026
34Straight Lines And Pair Of Straight Lines
If the equation $x^2 - ky^2 - 4x + 6y - 5 = 0$ represents a pair of straight lines, then their point of intersection is
MCQ+2 / -02026
35Straight Lines And Pair Of Straight Lines
The equation of a line passing through the point of the intersection of the lines $x - y + 1 = 0$ and $2x + 3y - 8 = 0$ and having x intercept $3$ is
MCQ+2 / -02026
36Straight Lines And Pair Of Straight Lines
If the slope of one of the two lines given by $\dfrac{x^2}{a} + \dfrac{2xy}{h} + \dfrac{y^2}{b} = 0$ is twice that of the other, then $h^2 : ab = $ ...
MCQ+2 / -02026
37Straight Lines And Pair Of Straight Lines
If the distance between the lines represented by $(x - 2y)^2 + k(x - 2y) = 0$ is $3$ units and $k > 0$ then the equations of the lines are
MCQ+2 / -02026
38Straight Lines And Pair Of Straight Lines
The line $2x+y=4$ intersects X and Y axes at points A and B respectively. Let $C(p, q)$ be the point such that the lines AC and BC are perpendicular. The distance of point C from the midpoint of segment AB is...
MCQ+2 / -02026
39Straight Lines And Pair Of Straight Lines
The equation $x^2-3 x y+2 y^2+3 x-5 y+2=0$ represents a pair of straight lines. If $\theta$ is the angle between them, then the value of $\cos \theta$ is equal to
MCQ+2 / -02025
40Straight Lines And Pair Of Straight Lines
If the line $3 x+4 y-24=0$ intersects X and Y axes in points A and B respectively then incentre of the triangle OAB where O is origin is
MCQ+2 / -02025
41Straight Lines And Pair Of Straight Lines
The line MN whose equation is $x-y-2=0$ cuts the X -axis at M and co-ordinates of N are $(4,2)$. The line MN is rotated about M through $45^{\circ}$ in anticlockwise direction. The equation of the line MN in the new position is
MCQ+2 / -02025
42Straight Lines And Pair Of Straight Lines
The circumcenter of the triangle formed by lines $x y+2 x+2 y+4=0$ and $x+y+2=0$ is
MCQ+2 / -02025
43Straight Lines And Pair Of Straight Lines
If the pair of lines $3 x^2-5 x y+\mathrm{p} y^2=0$ and $6 x^2-x y-5 y^2=0$ have one line common, then $\mathrm{p}=$
MCQ+2 / -02025
44Straight Lines And Pair Of Straight Lines
The acute angle between the line $4 x-2 y+13=0$ and the line which makes equal intercepts with the co-ordinate axes is
MCQ+2 / -02025
45Straight Lines And Pair Of Straight Lines
A line passes through $\mathrm{P}(-4,1)$ and meets the co-ordinate axes at points A and B . If P divides the segment AB internally in the ratio $1: 2$, then the equation of the line is
MCQ+2 / -02025
46Straight Lines And Pair Of Straight Lines
The joint equation of the bisector of the angle between the lines $2 x^2+11 x y+3 y^2=0$ is
MCQ+2 / -02025
47Straight Lines And Pair Of Straight Lines
The slopes of the lines represented by $6 x^2+2 \mathrm{hxy}+y^2=0$ are in the ratio $2: 3$, then $\mathrm{h}=$
MCQ+2 / -02025
48Straight Lines And Pair Of Straight Lines
The straight line passing through $(-3,6)$ and midpoint of the line segment joining the points $(4,-5)$ and ( $-2,9$ ) have inclination
MCQ+2 / -02025
49Straight Lines And Pair Of Straight Lines
The distance of the point $(1,2)$ from the line $x+y=0$ measured parallel to the line $3 x-y=2$ is
MCQ+2 / -02025
50Straight Lines And Pair Of Straight Lines
The joint equation of two lines passing through $(-2,3)$ and parallel to the bisectors of the angle between the co-ordinate axes is
MCQ+2 / -02025