Straight Lines and Pair of Straight Lines PYQs - Last 10 Years

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Last 10 Years Straight Lines and Pair of Straight Lines Questions

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1Straight Lines And Pair Of Straight Lines

The equation $x^2-3 x y+\lambda y^2+3 x-5 y+2=0$, where $\lambda$ is real number represents pair of lines If $\theta$ is acute angle between the lines, then $\frac{\operatorname{cosec}^2 \theta}{\sqrt{10}}=$

2Straight Lines And Pair Of Straight Lines

If the pair of straight lines $x y-x+y-1=0$ and the line $x+\mathrm{k} y-3=0$ are concurrent, then the value of $k$ is equal to

3Straight Lines And Pair Of Straight Lines

From the following options, the nearest line to the origin is ….

4Straight Lines And Pair Of Straight Lines

The circumradius of the triangle formed by the lines $x y+2 x+2 y+4=0$ and $x+y+2=0$ is

5Straight Lines And Pair Of Straight Lines

The joint equation of the bisectors of the angles between the lines $x=5$ and $y=3$ is

6Straight Lines And Pair Of Straight Lines

If the line $2 x+y=\mathrm{k}$ passes though the point which divides the line segment joining the points $(1,1)$ and $(2,4)$ internally in the ratio $3: 2$ then, $(k+1):(k-1)=$

7Straight Lines And Pair Of Straight Lines

The points $(1,3)$ and $(5,1)$ are two opposite vertices of a rectangle. The other two vertices are lie on the line $y=2 x+\mathrm{c}$ where c is the constant, then co-ordinates of other two vertices are

8Straight Lines And Pair Of Straight Lines

The distance between the lines represented by $16 x^2+9 y^2+48 x-24 x y-36 y+35=0$ is ......... units

9Straight Lines And Pair Of Straight Lines

The line passing through the point $(5,1, a)$ and $(3, \mathrm{~b}, 1)$ crosses the $y \mathrm{z}$-plane at $\left(0, \frac{17}{2}, \frac{-13}{2}\right)$, then the value of $2 a+3 b$ is

10Straight Lines And Pair Of Straight Lines

The distance between the lines represented by the equation $4 x^2+4 x y+y^2-6 x-3 y-4=0$ is

11Straight Lines And Pair Of Straight Lines

The acute angle between the diagonals of a parallelogram whose vertices are $\mathrm{A}(2,-1)$, $B(0,2), C(2,3)$ and $D(4,0)$ is

12Straight Lines And Pair Of Straight Lines

If the equation of the median through vertex $\mathrm{A}(3, \mathrm{k})$ of $\triangle \mathrm{ABC}$ with vertices $\mathrm{B}(2,1)$ and $\mathrm{C}(-4,5)$ is $x+4 y=\mathrm{p}$, then $\mathrm{k}=$ where p and k are constants

13Straight Lines And Pair Of Straight Lines

If the equation $\mathrm{k} x y+10 x+8 y+16=0$ represents a pair of lines, then

14Straight Lines And Pair Of Straight Lines

The point of intersection of the diagonals of the rectangle whose sides are contained in the lines $x=8, x=10, y=11$ and $y=12$ is

15Straight Lines And Pair Of Straight Lines

If $m_1$ and $m_2$ are the slopes of the lines represented by $a x^2+2 h x y+b y^2=0$ satisfying the condition $16 \mathrm{~h}^2=25 \mathrm{ab}$, then ............ .

16Straight Lines And Pair Of Straight Lines

A straight line through the origin $O$ meets the line $3 y=10-4 x$ and $8 x+6 y+5=0$ at the points $A$ and B respectively. Then O divides the segment $A B$ in the ratio

17Straight Lines And Pair Of Straight Lines

The perpendicular distance between the lines given by $(x-2 y+1)^2+\mathrm{k}(x-2 y+1)=0$ is $\sqrt{5}$, then $\mathrm{k}=$

18Straight Lines And Pair Of Straight Lines

The straight line, $2 x-3 y+17=0$ is perpendicular to the line passing through the points $(7,17)$ and $(15, \beta)$, then $\beta$ equals

19Straight Lines And Pair Of Straight Lines

If an equation $h x y+g x+f y+c=0$ represents a pair of lines, then

20Straight Lines And Pair Of Straight Lines

A line $4 x+y=1$ passes through the point $\mathrm{A}(2,-7)$ meets the line BC whose equation is $3 x-4 y+1=0$ at the point $B$. The equation of the line $A C$ so that $A B=A C$ is

21Straight Lines And Pair Of Straight Lines

The joint equation of pair of lines through the origin and making an angle of $\frac{\pi}{6}$ with the line $3 x+y-6=0$ is

22Straight Lines And Pair Of Straight Lines

If $4 a b=3 h^2$, then the ratio of the slope of lines represented by $a x^2+2 \mathrm{~h} x y+\mathrm{b} y^2=0$ is

23Straight Lines And Pair Of Straight Lines

The line L given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line K is parallel to line L and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between L and K is _________ units.

24Straight Lines And Pair Of Straight Lines

The acute angle between the lines $x \cos 30^{\circ}+y \sin 30^{\circ}=3$ and $x \cos 60^{\circ}+y \sin 60^{\circ}=5$ is

25Straight Lines And Pair Of Straight Lines

If $\mathrm{O}(0,0), \mathrm{A}(1,2)$ and $\mathrm{B}(3,4)$ are the vertices of triangle OAB , then the joint equation of the altitude and median drawn from O is

26Straight Lines And Pair Of Straight Lines

The combined equation of two lines through the origin and making an angle of $45^{\circ}$ with the line $3 x+y=0$, is

27Straight Lines And Pair Of Straight Lines

The line L given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line K is parallel to L and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between $L$ and $K$ is

28Straight Lines And Pair Of Straight Lines

The number of possible distinct straight lines passing through $(2,3)$ and forming a triangle with co-ordinate axes whose area is 12 sq . units are,

29Straight Lines And Pair Of Straight Lines

The equation of pair of lines $y=p x$ and $y=q x$ can be written as $(y-p x)(y-q x)=0$. Then the equation of the pair of the angle bisectors of the lines $x^2-4 x y-5 y^2=0$ is

30Straight Lines And Pair Of Straight Lines

The equation of the line passing through the point of intersection of the lines $3 x-y=5$ and $x+3 y=1$ and making equal intercepts on the axes is

31Straight Lines And Pair Of Straight Lines

The slopes of the lines given by $x^2+2 h x y+2 y^2=0$ are in the ratio $1: 2$, then $h$ is

32Straight Lines And Pair Of Straight Lines

If two lines $x+(a-1) y=1 \quad$ and $2 x+a^2 y=1(a \in R-\{0,1\})$ are perpendicular, then the distance of their point of intersection from the origin is

33Straight Lines And Pair Of Straight Lines

The diagonals of a parallelogram $A B C D$ are along the lines $x+3 y=4$ and $6 x-2 y=7$. Then ABCD must be a

34Straight Lines And Pair Of Straight Lines

If the equation $7 x^2-14 x y+p y^2-12 x+q y-4=0$ represents a pair of parallel lines then the value of $\sqrt{p^2+q^2-p q}$ is

35Straight Lines And Pair Of Straight Lines

Suppose that the points $(h, k),(1,2)$ and $(-3,4)$ lie on the line $l_1$. If a line $l_2$ passing through the points $(h, k)$ and $(4,3)$ is perpendicular to $l_1$, then $\left(\frac{k}{h}\right)$ equals

36Straight Lines And Pair Of Straight Lines

If $\frac{x^2}{\mathrm{a}}+\frac{2 x y}{\mathrm{~h}}+\frac{y^2}{\mathrm{~b}}=0$ represents a pair of straight lines and slope of one of the lines is twice that of the other, then $a b: h^2$ is

37Straight Lines And Pair Of Straight Lines

If $P_1$ and $P_2$ are perpendicular distances (in units) from point $(2,-1)$ to the pair of lines $2 x^2-5 x y+2 y^2=0$, then the value of $\mathrm{P}_1 \mathrm{P}_2$ is

38Straight Lines And Pair Of Straight Lines

The co-ordinates of the foot of perpendicular, drawn from the point $(-2,3)$ on the line $3 x-y-1=0$ are

39Straight Lines And Pair Of Straight Lines

If two sides of a square are $4 x+3 y-20=0$ and $4 x+3 y+15=0$, then the area of the square is

40Straight Lines And Pair Of Straight Lines

The value of $k$, if the slope of one of the lines given by $4 x^2+k x y+y^2=0$ is four times that of the other, is given by

41Straight Lines And Pair Of Straight Lines

If one of the lines represented by $a x^2+2 h x y+b y^2=0$ is perpendicular to $\mathrm{m} x+\mathrm{n} y=18$, then

42Straight Lines And Pair Of Straight Lines

Let $\mathrm{P} \equiv(-5,0), \mathrm{Q} \equiv(0,0)$ and $\mathrm{R} \equiv(2,2 \sqrt{3})$ be three points. Then the equation of the bisector of the angle $P Q R$ is

43Straight Lines And Pair Of Straight Lines

If the slope of one of the lines given by $\mathrm{K} x^2+6 x y+y^2=0$ is three times the order, then the value of $K$ is

44Straight Lines And Pair Of Straight Lines

The joint equation of two lines through the origin, each making an angle with measure of $30^{\circ}$ with the positive Y -axis, is

45Straight Lines And Pair Of Straight Lines

The joint equation of pair of lines through the origin, each of which makes an angle of $30^{\circ}$ with Y -axis, is

46Straight Lines And Pair Of Straight Lines

A straight line L through the point $(3,-2)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3} x+y=1$. If L also intersects the X -axis, then the equation of $L$ is

47Straight Lines And Pair Of Straight Lines

$\triangle \mathrm{OAB}$ is formed by the lines $x^2-4 x y+y^2=0$ and the line $A B$. The equation of line $A B$ is $2 x+3 y-1=0$. Then the equation of the median of the triangle drawn from the origin is

48Straight Lines And Pair Of Straight Lines

Let a line intersect the co-ordinate axes in points $A$ and $B$ such that the area of the triangle $O A B$ is 12 sq. units. If the line passes through the point $(2,3)$, then the equation of the line is

49Straight Lines And Pair Of Straight Lines

The number of integer values of $m$, for which $x$-coordinate of the point of intersection of the lines $3 x+4 y=9$ and $y=m x+1$ is also an integer, is

50Straight Lines And Pair Of Straight Lines

If the length of the perpendicular to a line from the origin is $2 \sqrt{2}$ units, which makes an angle of $135^{\circ}$ with the X -axis, then the equation of line is