Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 33

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The equation of the circle, orthogonal to both the circles $x^{2} + y^{2} + 3 x - 5 y + 6 = 0$ and $4 x^{2} + 4 y^{2} - 28 x + 29 = 0$ and whose centre lies on the line $3 x + 4 y + 1 = 0$ is

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Important Questions on Conic Section

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 34

The equation of a circle which touches the line

x + y = 5

at the point

(- 2, 7)

and cuts the circle

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

orthogonally 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

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 36

If centre of a circle lies on the line

2 x - 6 y + 9 = 0

and it cuts the circle

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

orthogonally then the circle passes through two fixed points

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 37

The radical centre of three circles described on the three sides

4 x - 7 y + 10 = 0, x + y - 5 = 0

and

7 x + + 4 y - 15 = 0

of a triangle as diameters is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 38

The equation of the circle passing through

(1, 0)

and

(0, 1)

and having smallest possible radius is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 39

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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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 40

The locus of the centre of a circle, which touches externally the circle

x^{2} + y^{2} - 6 x - 6 y + 14 = 0

and also touches the

y

-axis, is given by the equation

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 41

The locus of the centre of a circle of radius

2

which rolls on the outside of the circle, is

x^{2} + y^{2} + 3 x - 6 y - 9 = 0

is