Straight Lines And Pair Of Straight Lines - Coordinate Geometry - Mathematics Previous Year Questions

1

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 10TH MAY EVENING SHIFT

The equation of the straight line whose slope is $\frac{-2}{3}$ and which divides the line segment joining $(1,2),(-3,5)$ in the ratio $4: 3$ externally is

A

$2 x+3 y-12=0$

B

$3 x+2 y+27=0$

C

$2 x+3 y-9=0$

D

$2 x+3 y+12=0$

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2

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 10TH MAY EVENING SHIFT

By shifting the origin to the point $(h, 5)$ by the translation of coordinate axes, if the equation $y=x^{3}-9 x^{2}+c x-d$ transforms to $Y=X^{3}$, then $\left(d-\frac{c}{h}\right)=$

A

0

B

13

C

11

D

25

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3

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 10TH MAY EVENING SHIFT

The combined equation of a possible pair of adjacent sides of a square with area 16 square units whose centre is the point of intresection of the lines $x+2 y-3=0$ and $2 x-y-1=0$ is

A

$(2 x-y-1+4 \sqrt{5})(x+2 y-3+4 \sqrt{5})=0$

B

$(2 x-y-1-4 \sqrt{5})(x+2 y-4 \sqrt{5})=0$

C

$(2 x-y-2 \sqrt{5})(x+2 y+2 \sqrt{5})=0$

D

$(2 x-y-1-2 \sqrt{5})(x+2 y-3+2 \sqrt{5})=0$

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4

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 10TH MAY EVENING SHIFT

If the line $2 x+b y+5=0$ forms an equilateral to triangle with $a x^{2}-96 b x y+k y^{2}=0$, then $a+3 k=$

A

$3 b$

B

192

C

$4 b^{2}$

D

102

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5

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 10TH MAY EVENING SHIFT

$7 x+y-24=0$ and $x+7 y-24=0$ represent the equal sides of an isosceles triangle. If the third side passes through $(-1,1)$ then, a possible equation for the third side is

A

$3 x-y=-4$

B

$x+y=0$

C

$x-2 y=-3$

D

$3 x+y=-2$

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6

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT

If $(2,-1)$ is the point of intersection of the pair of lines $2 x^2+a x y+3 y^2+b x+c y-3=0$, then $3 a+2 b+c=$

A

11

B

0

C

1

D

21

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7

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT

If $Q$ and $R$ are the images of the point $P(2,3)$ with respect to the lines $x-y+2=0$ and $2 x+y-2=0$ respectively, then $Q$ and $R$ lie on

A

the same side of the line $2 x+y-2=0$

B

the opposite sides of the line $2 x-y-2=0$

C

the same side of the line $x+y+2=0$

D

the opposite sides of the line $x-y+2=0$

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8

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT

The line $2 x+y-3=0$ divides the line segment joining the points $A(1,2)$ and $B(-2,1)$ in the ratio $a: b$ at the point $C$. If the point $C$ divides the line segment joining the points $P\left(\frac{b}{3 a},-3\right)$ and $Q\left(-3,-\frac{b}{3 a}\right)$ in the ratio $p: q$, then $\frac{p}{q}+\frac{q}{p}=$

A

$\frac{29}{10}$

B

$\frac{17}{10}$

C

6

D

5

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9

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT

If the distance from a variable point $P$ to the point $(4,3)$ is equal to the perpendicular distance from $P$ to the line $x+2 y-1=0$, then the equation of the locus of the point $P$ is

A

$4 x^2+4 x y+y^2-38 x+26 y+124=0$

B

$4 x^2-4 x y+y^2-38 x-26 y+124=0$

C

$4 x^2-4 x y+y^2+38 x+26 y+124=0$

D

$4 x^2-4 x y+y^2-38 x+26 y+124=0$

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10

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT

$(0, k)$ is the point to which the origin is to be shifted by the translation of the axes so as to remove the first degree terms from the equation $a x^2-2 x y+b y^2-2 x+4 y+1=0$ and $\frac{1}{2} \tan ^{-1}(2)$ is the angle through which the coordinate axes are to be rotated about the origin to remove the $x y$-term from the given equation, then $a+b=$

A

1

B

-2

C

3

D

-4

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11

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT

$\beta$ is the angle made by the perpendicular drawn from origin to the line $L \equiv x+y-2=0$ with the positive $X$-axis in the anticlockwise direction. If $a$ is the $X$-intercept of the line $L=0$ and $p$ is the perpendicular distance from the origin to the line $L=0$, then $a \tan \beta+p^2=$

A

1

B

2

C

3

D

4

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12

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT

$(a, b)$ is the point to which the origin has to be shifted by translation of axes so as to remove the first-degree terms from the equation $2 x^{2}-3 x y+4 y^{2}+5 y-6=0$. If the angle by which the axes are to be rotated in positive direction about the origin to remove the $x y$-term from the equation $a x^{2}+23 a b x y+b y^{2}=0$ is $\theta$, then $\tan 2 \theta=$

A

$\frac{\pi}{4}$

B

60

C

$\frac{\pi}{3}$

D

15

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13

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT

The area of the parallelogram formed by the lines $L_{1} \equiv \lambda x+4 y+2=0, L_{2} \equiv 3 x+4 y-3=0$, $L_{3} \equiv 2 x+\mu y+6=0, L_{4} \equiv 2 x+y+3=0$, where $L_{1}$ is parallel to $L_{2}$ and $L_{3}$ is parallel to $L_{4}$ is

A

9

B

7

C

5

D

3

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14

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT

If the angle between the pair of lines given by the equation $a x^{2}+4 x y+2 y^{2}=0$ is $45^{\circ}$, then the possible values of $a$

A

are -3 or 21

B

are $-6 \pm 4 \sqrt{3}$

C

are $-6 \pm 24 \sqrt{2}$

D

do not exist

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15

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT

$A(1,-2), B(-2,3), C(-1,-3)$ are the vertices of a $\triangle A B C . L_{1}$ is the perpendicular drawn from $A$ to $B C$ and $L_{2}$ is the perpendicular bisector of $A B$. If $(l, m)$ is the point of intersection of $L_{1}$ and $L_{2}$, then $26 m-3=$

A

261

B

$89 /$

C

$13 /$

D

431

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16

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 9TH MAY EVENING SHIFT

If the ratio of the distances of a variable point $P$ from the point $(1,1)$ and the line $x-y+2=0$ is $1: \sqrt{2}$, then the equation of the locus of $P$ is

A

$x^2+2 x y+y^2-8 x=0$

B

$3 x^2+2 x y+3 y^2-12 x-4 y+4=0$.

C

$x^2+2 x y+y^2-12 x+4 y+4=0$

D

$x^2+2 x y+y^2-8 x+8 y=0$

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17

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 9TH MAY EVENING SHIFT

The slope of one of the pair of lines $2 x^2+h x y+6 y^2=0$ is thrice the slope of the other line, then $h=$

A

$\pm 16$

B

$\pm 9$

C

$\pm 18$

D

$\pm 8$

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18

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 9TH MAY EVENING SHIFT

$L \equiv x \cos \alpha+y \sin \alpha-p=0$ represents a line perpendicular to the line $x+y+1=0$. If $p$ is positive, $\alpha$ lies in the fourth quadrant and perpendicular distance from $(\sqrt{2}, \sqrt{2})$ to the line, $L=0$ is 5 units, then $p=$

A

5

B

$\frac{5}{2}$

C

10

D

$\frac{15}{2}$

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19

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 9TH MAY EVENING SHIFT

If the origin is shifted to the point $\left(\frac{3}{2},-2\right)$ by the translation of axes, then the transformed equation of $2 x^2+4 x y+y^2+2 x-2 y+1=0$ is

A

$4 x^2+8 x y+2 y^2-16=0$

B

$2 x^2-4 x y+y^2=0$

C

$4 x^2+8 x y+2 y^2+9=0$

D

$2 x^2-4 x y+y^2+16=0$

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20

2024 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines

TG EAPCET 2024 ONLINE 9TH MAY EVENING SHIFT

$L_1 \equiv 2 x+y-3=0$ and $L_2 \equiv a x+b y+c=0$ are two equal sides of an isosceles triangle. If $L_3 \equiv x+2 y+1=0$ is the third side of this triangle and $(5,1)$ is a point on $L_2=$ 0 , then $\frac{b^2}{|a c|}=$

A

$\frac{121}{2}$

B

$\frac{49}{52}$

C

$\frac{81}{49}$

D

$\frac{25}{4}$

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