Circle - Coordinate Geometry - Mathematics Previous Year Questions

1

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 10TH MAY EVENING SHIFT

If $m$ is the slope and $P(8, \beta)$ is the mid-point of a chord of contact of the circle $x^{2}+y^{2}=125$, then the number of values of $\beta$ such that $\beta$ and $m$ are integers is

A

2

B

4

C

6

D

8

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2

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 10TH MAY EVENING SHIFT

The equation of a circle which passes through the points of intersection of the circles $2 x^{2}+2 y^{2}-2 x+6 y-3=0, x^{2}+y^{2}+4 x+2 y+1=0$ and whose centre lies on the common chord of these circles is

A

$2 x^{2}+2 y^{2}-3 x+4 y-2=0$

B

$x^{2}+y^{2}+2 x+5 y-2=0$

C

$3 x^{2}+3 y^{2}-2 x+4 y-3=0$

D

$4 x^{2}+4 y^{2}+6 x+10 y-1=0$

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3

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 10TH MAY EVENING SHIFT

A rhombus is inscribed in the region common to the two circles $x^{2}+y^{2}-4 x-12=0$ and $x^{2}+y^{2}+4 x-12=0$. If the line joining the centres of these circles and the common chord of them are the diagonals of this rhombus, then the area (in sq units) of the rhombus is

A

$16 \sqrt{3}$

B

$4 \sqrt{3}$

C

$12 \sqrt{3}$

D

$8 \sqrt{3}$

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4

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 10TH MAY EVENING SHIFT

A rectangle is formed by the lines $x=4, x=-2, y=5, y=-2$ and a circle is drawn through the vertices of this rectangle. The pole of the line $y+2=0$ with respect to this circle is

A

$\left(1, \frac{-85}{14}\right)$

B

$\left(1, \frac{-32}{7}\right)$

C

$(-2,-2)$

D

$(1,-4)$

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5

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 10TH MAY EVENING SHIFT

The equation of the circle passing through the origin and cutting the circles $x^{2}+y^{2}+6 x-15=0$ and $x^{2}+y^{2}-8 y-10=0$ orthogonally is

A

$2 x^{2}+2 y^{2}-5 x+10 y=0$

B

$x^{2}+y^{2}-2 x+5 y=0$

C

$2 x^{2}+2 y^{2}-10 x+5 y=0$

D

$x^{2}+y^{2}-5 x+2 y=0$

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6

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 10TH MAY EVENING SHIFT

If the equation of the circle which cuts each of the circles $x^{2}+y^{2}=4, x^{2}+y^{2}-6 x-8 y+10=0$ and $x^{2}+y^{2}+2 x-4 y-2=0$ at the extremities of a diameter of these circles is $x^{2}+y^{2}+2 g x+2 f y+c=0$, then $g+f+c=$

A

9

B

-9

C

12

D

-12

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7

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT

$(1, k)$ is a point on the circle passing through the points $(-1,1),(0,-1)$ and $(1,0)$. If $k \neq 0$, then $k=$

A

$\frac{1}{2}$

B

$\frac{1}{3}$

C

$-\frac{1}{3}$

D

$-\frac{1}{2}$

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8

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT

If the tangents $x+y+k=0$ and $x+a y+b=0$ drawn to the circle $S=x^2+y^2+2 x-2 y+1=0$ are perpendicular to each other and $k, b$ are both greater than 1 , then $b-k=$

A

$\sqrt{2}$

B

0

C

2

D

$2 \sqrt{2}$

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9

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT

If $(h, k)$ is the internal centre of similitude of the circles $x^2+y^2+2 x-6 y+1=0$ and $x^2+y^2-4 x+2 y+4=0$, then $4 h=$

A

0

B

3

C

1

D

5

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10

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT

$x^2+y^2+2 x-6 y-6=0$ and $x^2+y^2-6 x-2 y+k=0$ are two intersecting circles and $k$ is not an integer. If $\theta$ is the angle between the two circles and $\cos \theta=\frac{-5}{24}$, then $k=$

A

$\frac{6}{5}$

B

$\frac{74}{9}$

C

$\frac{37}{3}$

D

$\frac{53}{7}$

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11

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT

The slope of a common tangent to the circles $x^2+y^2-4 x-8 y+16=0$ and $x^2+y^2-6 x-16 y+64=0$ is

A

0

B

$\frac{15}{8}$

C

1

D

$\frac{17}{4}$

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12

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT

If $(p, q)$ is the centre of the circle which cuts the three circles $x^2+y^2-2 x-4 y+4=0, x^2+y^2+2 x-4 y+1=0$ and $x^2+y^2-4 x-2 y-11=0$ orthogonally, then $p+q=$

A

9

B

$\frac{35}{4}$

C

$\frac{15}{2}$

D

7

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13

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT

$P$ and $Q$ are the points of trisection of the line segment joining the points $(3,-7)$ and $(-5,3)$. If $P Q$ subtends right angle at a variable point $R$, then the locus of $R$ is

A

a circle with radius $\frac{\sqrt{41}}{3}$

B

a circle with radius $\sqrt{409}$

C

a pair of straight lines passing through $(-1,-2)$

D

a pair of straight lines passing through $(1,2)$

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14

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT

$x-2 y-6=0$ is a normal to the circle $x^{2}+y^{2}+2 g x+2 f y-8=0$. If the line $y=2$ touches this circle, then the radius of the circle can be

A

$\sqrt{32}$

B

6

C

4

D

$\sqrt{18}$

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15

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT

A circle passing through the points $(1,1)$ and $(2,0)$ touches the line $3 x-y-1=0$. If the equation of this circle is $x^{2}+y^{2}+2 g x+2 f y+c=0$, then a possible value of $g$ is

A

$-\frac{5}{2}$

B

$-\frac{3}{2}$

C

6

D

-5

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16

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT

A circle passes through the points $(2,0)$ and $(1,2)$. If the power of the point $(0,2)$ with respect to this circle is 4 , then the radius of the circle is

A

2

B

$\sqrt{\frac{5}{2}}$

C

$\sqrt{5}$

D

4

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17

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT

A circle $S$ passes through the points of intersection of the circles $x^{2}+y^{2}-2 x-3=0$ and $x^{2}+y^{2}-2 y=0$. If $x+y+1=0$ is a tangent to the circle $S$, then equation of $S$ is

A

$2 x^{2}+2 y^{2}+2 x+2 y+3=0$

B

$2 x^{2}+2 y^{2}-2 x-2 y+3=0$

C

$x^{2}+y^{2}-2 x-2 y+3=0$

D

$2 x^{2}+2 y^{2}-2 x-2 y-3=0$

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18

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT

If $A(1,2), B(2,1)$ are two vertices of an acute angled triangle and $S(0,0)$ is its circumcenter, then the angle subtended by $A B$ at the third vertex is

A

$\tan ^{-1}\left(\frac{1}{3}\right)$

B

$\tan ^{-1}\left(\frac{1}{2}\right)$

C

$\frac{\pi}{4}$

D

$\frac{\pi}{6}$

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19

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT

The line $x+y+1=0$ intersects the circle $x^{2}+y^{2}-4 x+2 y-4=0$ at the points $A$ and $B$. If $M(a, b)$ is the mid-point of $A B$, then $a-b=$

A

0

B

1

C

2

D

3

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20

2024 · Mathematics · Coordinate Geometry · Circle

TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT

If the common chord of the circles $x^{2}+y^{2}-2 x+2 y+1=0$ and $x^{2}+y^{2}-2 x-2 y-2=0$ is the diameter of a circle $S$, then the center of the circles is

A

$\left(\frac{1}{2},-\frac{3}{4}\right)$

B

$\left(1,-\frac{3}{4}\right)$

C

$\left(1, \frac{3}{4}\right)$

D

$\left(-\frac{1}{2},-\frac{3}{4}\right)$

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