Straight Lines and Pair of Straight Lines PYQs - Last 5 Years
TS EAMCET / Mathematics / Coordinate Geometry / 136 recent questions
MathematicsCoordinate Geometry2021-2025
Practice 136 TS EAMCET 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 36 of 136 filtered questions.
1Straight Lines And Pair Of Straight Lines
The number of real values of $\alpha$ for which the pair of lines represented by $\left(\alpha^2+12|\alpha|\right) x^2+6 x y+(18-21|\alpha|) y^2=0$ are at right angles to each other, is
MCQ+1 / -02022
2Straight Lines And Pair Of Straight Lines
If the lines $L_1 \equiv x-2 y+3=0, L_2 \equiv 2 x+y+1=0$ and $L_3 \equiv 3 x+y+c=0$ are concurrent and $\theta$ is the acute angle between the lines $L_1=0$ and $L_3=0$, then $\tan \theta=$
MCQ+1 / -02022
3Straight Lines And Pair Of Straight Lines
If $3 x+6 y+2=0, x+y+1=0,2 x-y+3=0$ are three given lines, then the point $\left(\frac{-4}{3}, \frac{1}{3}\right)$ is
MCQ+1 / -02022
4Straight Lines And Pair Of Straight Lines
If the lengths of the perpendiculars drawn from a point $(a, b)$ to the lines $2 x+3 y+4=0$ and $3 x-2 y+4=0$ are same, then the point $(a, b)$ lies on the line
MCQ+1 / -02022
5Straight Lines And Pair Of Straight Lines
The line $x+2 y-c=0$ meets the curve $x^2+y^2-3 x-6 y+3=0$ at two points $P$ and $Q$ and $\angle P O Q=\frac{\pi}{2}$, where $O$ is the origin. Then, $2 c^2-15 c=$
MCQ+1 / -02022
6Straight Lines And Pair Of Straight Lines
If $\theta$ is the acute angle between the pair of lines $12 x^2+2 h x y+7 y^2=0$ and $\tan \theta=\frac{8}{19}$, then $h=$
MCQ+1 / -02022
7Straight Lines And Pair Of Straight Lines
By rotating the axes through an angle of $30^{\circ}$ in the anti-clockwise direction about the origin, the equation $4 x^2+12 x y+9 y^2+6 x+9 y+2=0$ becomes $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$ becomes, then
MCQ+1 / -02022
8Straight Lines And Pair Of Straight Lines
Let the line $L$ drawn perpendicular to the lines $2 x-3 y+4=0$ and $6 x-9 y+7=0$ meet them at $A$ and $B$, respectively. If $P(\mathrm{l}, \mathrm{l})$ is a point on $L$, then the ratio in which $P$ divides $A B$ is
MCQ+1 / -02022
9Straight Lines And Pair Of Straight Lines
The orthocentre of the triangle formed by the points $(1,3),(-3,5)$ and $(5,-1)$ is
MCQ+1 / -02022
10Straight Lines And Pair Of Straight Lines
If the line $2 x-y-4=0$ divides the line segment joining the points $(2,-1)$ and $(1,-4)$ at the point $(a, b)$ in the ratio $m: n$, then $4\left(a-b\left(\frac{m}{n}\right)^2\right)=$
MCQ+1 / -02022
11Straight Lines And Pair Of Straight Lines
If the lines joining the origin to the points of intersection of the line $x+y=k$ and the curve $x^2+y^2-2 x-4 y+2=0$ are at right angles, then the sum of all the possible values of $k$ is
MCQ+1 / -02022
12Straight Lines And Pair Of Straight Lines
$\frac{x^2}{a}+\frac{x y}{h}+\frac{y^2}{b}=0(a \neq 0, h \neq 0, b \neq 0)$ represents two coincident lines if
MCQ+1 / -02022
13Straight Lines And Pair Of Straight Lines
If $\alpha x^2+2 \gamma x y+\beta y^2=0$ is the equation of pair of lines passing through the origin and perpendicular to the pair of lines $b h x^2+a b x y+a h y^2=0(a \neq 0, b \neq 0)$, then $\alpha \beta / \gamma^2=$
MCQ+1 / -02022
14Straight Lines And Pair Of Straight Lines
The distance between the points of concurrency of the two families of straight lines given by $x+(5 \lambda+1) y+1-3 \lambda=0$ and $(5 \mu+2) x-3 y+3+6 \mu=0$ is
MCQ+1 / -02022
15Straight Lines And Pair Of Straight Lines
If $f(x, y)=0$ is the combined equation of the lines joining the origin to the points where the line $4 x-6 y-2=0$ meets the curve $3 x^2-4 x y+5 y^2-2 x+y-6=0$, then $\frac{f(1,-1)}{f(-1,-1)}=$
MCQ+1 / -02022
16Straight Lines And Pair Of Straight Lines
If $\theta$ is the acute angle between the pair of lines $H \equiv a x^2-x y+b y^2=0, \tan \theta=5$ and $(1,-1)$ is a point on $H=0$, then $a^2+a b+b^2=$
MCQ+1 / -02022
17Straight Lines And Pair Of Straight Lines
If the algebraic sum of the perpendicular distances from the points $(2,0),(0,2)$ and $(1,1)$ to a variable line is zero, then the variable line always passes through a fixed point. The coordinates of that point are
MCQ+1 / -02022
18Straight Lines And Pair Of Straight Lines
If a straight line $L$ passing through the point $(5,-3)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3} x+y-9=0$ and $L$ intersects $X$-axis, then the equation of $L$ is
MCQ+1 / -02022
19Straight Lines And Pair Of Straight Lines
For $a, b, c \in R$, if $6 a^2-3 b^2-c^2+7 a b-a c+4 b c=0$ and $|a|+|b| \neq 0$, then all the lines given by $a x+b y+c=0$ are
MCQ+1 / -02022
20Straight Lines And Pair Of Straight Lines
Let $\alpha, \beta$ and $\gamma$ be three non-zero real constants and $a, b$ and $c$ be three arbitrary real numbers which satisfy $\alpha a+\beta b+\gamma c=0$. Then, the point of concurrence of the family of lines $a x+b y+c=0$ is
MCQ+1 / -02022
21Straight Lines And Pair Of Straight Lines
The equation of the pair of straight lines passing through the point $(2,3)$ and perpendicular to the pair of lines $3 x^2-4 x y+5 y^2=0$ is $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$, then $a+b+c+f+g+h=$
MCQ+1 / -02022
22Straight Lines And Pair Of Straight Lines
Let $L_1, L_2$ be the lines represented by the equation $4 x^2-5 x y+3 y^2=0$. Let $L_3, L_4$ be two lines passing through the point $(4,3)$ such that $L_3$ and $L_4$ are perpendicular to $L_1$ and $L_2$ respectively. If the combined equati...
MCQ+1 / -02022
23Straight Lines And Pair Of Straight Lines
If the incentre and the circumcentre of the triangle formed by the lines $x=2,4 x+3 y+7=0$ and $y=3$ are $I$ and $S$ respectively, then $I S=$
MCQ+1 / -02022
24Straight Lines And Pair Of Straight Lines
The equation $x^2-y^2+a x+b=0$ represents a pair of lines for the ordered pair $(a, b)=$
MCQ+1 / -02022
25Straight Lines And Pair Of Straight Lines
$a x^2-4 x y-2 y^2=0$ represents a pair of lines. If $\theta$ is the angle between these lines, $\cos \theta=\frac{1}{5}$ and the possible values of ' $a$ ' are $a_1$ and $a_2\left(a_1
MCQ+1 / -02022
26Straight Lines And Pair Of Straight Lines
Let $A(5,-3), B(3,-2), C(-1,5)$ be three points. If $P$ is a point satisfying the condition $P A^2+2 P B^2=3 P C^2$, then a point that lies on the locus of $P$ is
MCQ+1 / -02022
27Straight Lines And Pair Of Straight Lines
If the line $x-y+1=0$ cuts the lines $2 x+2 y+3=0$ and $3 x+3 y+2=0$ at the points $A$ and $B$ respectively, then $A B=$
MCQ+1 / -02022
28Straight Lines And Pair Of Straight Lines
If $\theta$ is the acute angle between the lines $\frac{x}{a}+\frac{y}{b}=1, \frac{x}{b}+\frac{y}{a}=1$, then $\sin \theta=$
MCQ+1 / -02022
29Straight Lines And Pair Of Straight Lines
If $Q$ is the image of the point $P(1,1)$ with respect to the straight line $x+y+1=0$, then the length of the perpendicular drawn from $Q$ to the line $3 x-4 y+3=0$ is
MCQ+1 / -02022
30Straight Lines And Pair Of Straight Lines
If the lines $L_1 \equiv 2 x+y+3=0, L_2 \equiv k x+2 y-3=0$ and $L_3 \equiv 3 x-2 y+1=0$ are concurrent then the cosine of the acute angle between the lines $L_2=0$ and $2 x-5 y+7=0$ is
MCQ+1 / -02022
31Straight Lines And Pair Of Straight Lines
If the line $2 x-3 y+4=0$ divides the line segment joining the points $A(-2,3)$ and $B(3,-2)$ in the ratio $m: n$, then the point which divides $A B$ in the ratio $-4 m: 3 n$ is
MCQ+1 / -02022
32Straight Lines And Pair Of Straight Lines
If the slope of one of the lines represented by $5 x^2+\frac{40}{3} x y+k y^2=0$ is 3 , then the angle between the pair of lines is
MCQ+1 / -02022
33Straight Lines And Pair Of Straight Lines
If $L$ is a line passing through the point $(-1,1)$ and parallel to the common line of the pairs of lines $6 x^2-x y-12 y^2=0$ and $15 x^2+14 x y-8 y^2=0$, then the equation of pair of lines joining the origin to the points of intersection ...
MCQ+1 / -02022
34Straight Lines And Pair Of Straight Lines
The centroid of the triangle formed by the lines $x-3 y+3=0, x+3 y+3=0 x+y-1=0$ is
MCQ+1 / -02022
35Straight Lines And Pair Of Straight Lines
If a line $L$ is common to the pairs of lines $6 x^2-x y-12 y^2=0$ and $15 x^2+14 x y-8 y^2=0$ then the combined equation the other two lines is
MCQ+1 / -02022
36Straight Lines And Pair Of Straight Lines
The transformed equation of $3 X^2+4 X Y+Y^2-8 X-4 Y-4=0$ is $f(X, Y)=a X^2+2 h X Y+b Y^2+c=0$ when the origin is shifted to a new point by the translation of axes. Then, $f(1,1)=$
MCQ+1 / -02022