Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 20

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IMPORTANT

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Let $C$ be the circle with centre $(0, 0)$ and radius $3$ units. The equation of the locus of the mid-points of the chords of the circle $C$ that subtend an angle of $\frac{2 π}{3}$ at its centre, is

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Important Questions on Circle

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 21

If the circles

x^{2} + y^{2} + 2 a x + c y + a = 0

and

x^{2} + y^{2} - 3 a x + d y - 1 = 0

intersect at two distinct points

P

and

Q,

then the line

5 x + b y - a = 0

passes through

P

and

Q

for

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 22

If a circle passes through the point

(a, b)

and cuts the circle

x^{2} + y^{2} = p^{2}

orthogonally, then the equation of the locus of its centre is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 23

If a circle passes through the point

(a, b)

and cuts the circle

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

orthogonally, then the locus of its centre is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 24

A variable circle passes through the fixed point

A (p, q)

and touches

x

-axis. The locus of other end of the diameter through

A

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 25

If the lines

2 x + 3 y + 1 = 0

and

3 x - y - 4 = 0

lie along the diameter of a circle of circumference

10 π,

then equation of the circle is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 26

The intercept on the line

y = x

by the circle

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

is

A B

. Then, the equation of a circle on

A B

as a diameter is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 27

If the two circles

{(x - 1)}^{2} + {(y - 3)}^{2} = r^{2}

and

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

intersect in two distinct points, then

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IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 28

The greatest distance of point

P (10, 7)

from the circle

x^{2} + y^{2} - 4 x - 2 y - 20 = 0

is