EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Circle>TS EAMCET 2020 (9-Sep Shift-1)>Q 13

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The area (in sq. units) of the triangle formed by the two tangents drawn from the extremal point $O (0, 0)$ to the circle $x^{2} + y^{2} - 2 g x - 2 h y + h^{2} = 0$ and their chord of contact is

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Important Questions on Circle

MEDIUM

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Circle>TS EAMCET 2018 (04-May Shift-1)>Q 14

If the chord

L \equiv y - m x - 1 = 0

of the circle

S \equiv x^{2} + y^{2} - 1 = 0

touches the circle

S_{1} = x^{2} + y^{2} - 4 x + 1 = 0

, then the possible points for which

L = 0

is a chord of contact of

S = 0

are

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Circle>TS EAMCET 2019 (03-May Shift-2)>Q 15

The lines represented by

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

are normals to a circle

S = 0

. If this circle touches the circle

S^{'} \equiv x^{2} + y^{2} - 2 x + 2 y - 7 = 0

externally, then the equation of the chord of contact of centre of

S^{'} = 0

with respect to

S = 0

is

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Circle>TS EAMCET 2021 (04-Aug Shift-1)>Q 16

The locus of the mid points of the chords of the circle

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

drawn from a point

(0, 0)

on it is

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Circle>TS EAMCET 2020 (9-Sep Shift-1)>Q 17

Consider the circles

S_{1} : x^{2} + y^{2} + 2 x + 8 y - 23 = 0

and

S_{2} : x^{2} + y^{2} - 4 x + 10 y + 19 = 0

If the polars of the centre of a circle with respect to the another circle are

L_{1}

and

L_{2}

, then

L_{1}, L_{2}

are

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Circle>TS EAMCET 2021 (04-Aug Shift-2)>Q 18

The polars of

(- 1, 2)

with respect to the two circles

S_{1} \equiv x^{2} + y^{2} + 6 y + 7 = 0

and

S_{2} \equiv x^{2} + y^{2} + 6 x + 1 = 0

are

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Circle>TS EAMCET - 5 August 2021 Shift 2>Q 19

If the points

(2, 3)

and

(K, - 2)

are conjugate with respect to the circle

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

, then

K =

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Circle>TS EAMCET 2020 (9-Sep Shift-1)>Q 20

If the circle

S \equiv x^{2} + y^{2} - 4 = 0

intersects another circle

S^{'} = 0

of radius

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

in such a manner that the common chord is of maximum length with slope equal to

\frac{1}{4},

then the centre of

S^{'} = 0

is

HARD

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Circle>TS EAMCET 2020 (9-Sep Shift-1)>Q 21

If the angle between the circles

x^{2} + y^{2} - 4 x - 6 y + k = 0

and

x^{2} + y^{2} + 8 x - 4 y + 11 = 0

is

\frac{π}{3},

then a value of

k

is