Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 12.3>Q 24

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Consider three circles $x^{2} + y^{2} = 1, x^{2} + y^{2} - 8 x + 15 = 0, x^{2} + y^{2} + 10 y + 24 = 0 .$ The point from which tangents of equal length can be drawn to all these three circles is

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Important Questions on Conic Section

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 12.3>Q 25

Interval of

r

for which

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

and

x^{2} + y^{2} - 6 x - 8 y + 9 = 0

cut at two distinct points is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 12.3>Q 26

Number of common real tangents that can be drawn to the circles

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

and

x^{2} + y^{2} - 8 x - 8 y + 14 = 0

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 12.3>Q 27

The equation of a chord of the circle

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

is given by

x + 2 y = 0 .

The equation of the circle described on this chord as diameter is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 12.3>Q 28

A circle

S

of radius

2

units lies in the first quadrant and touches both the coordinate axes. The equation of the circle with centre at

(6, 5)

and touching the circle

S

externally is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 12.4>Q 29

Locus of the middle points of chords of the circle

x^{2} + y^{2} = 16

which subtend a right angle at the centre is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 12.4>Q 30

The locus of the middle points of the chords of the circle

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

which pass through

(3, 4)

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 12.4>Q 31

Locus of centres of the circles which touch the two circles

x^{2} + y^{2} = 16

and

x^{2} + y^{2} = 16 x

externally is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 35

The locus of the centre of the circles which cut the circles

x^{2} + y^{2} + 4 x - 6 y + 9 = 0

and

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

orthogonally is