Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-1>Q 61

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The equation of the common tangent to the circle $x^{2} + y^{2} - 4 x - 6 y - 12 = 0$ and $x^{2} + y^{2} + 6 x + 18 y + 26 = 0$ at their point of contact is

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Important Questions on Circle

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-1>Q 62

The equation to the circle cutting orthogonally the three circles

x^{2} + y^{2} - 2 x + 3 y - 7 = 0, x^{2} + y^{2} + 5 x - 5 y + 9 = 0

and

x^{2} + y^{2} + 7 x - 9 y + 29 = 0

, is

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-1>Q 63

The length of a common internal tangent to two circle is

7

and that of a common external tangent is

11

. Then the product of the radii of the two circles is

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-1>Q 64

The locus of the centre of the circle which bisects the circumferences of the circles

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

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-1>Q 65

Equation of a circle drawn on the chord

x \cos α + y \sin α = p

of the circle

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

as its diameter, is

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-1>Q 66

Find the equation of the circle which passes through the point

(1, 1) &

which touches the circle

x^{2} + y^{2} + 4 x - 6 y - 3 = 0

at the point

(2, 3)

on it.

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-1>Q 67

Find the equation of circle touching the line

2 x + 3 y + 1 = 0

at

(1, - 1)

and cutting orthogonally the circle having line segment joining

(0, 3)

and

(- 2, - 1)

as diameter.

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-1>Q 68

Equation of the circle which passes through the point

(- 1, 2) &

touches the circle

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

at origin, is

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-1>Q 69

Two circles are drawn through the point

(a, 5 a)

and

(4 a, a)

to touch the axis of

{}^{'}y^{'} .

They intersect at an angle of

θ

then

\tan θ

is