Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 58

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The radius of the circle passing through the point of intersection of ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ and $x^{2} - y^{2} = 0$ 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 61

The angle between the two asymptotes of the hyperbola

\frac{x^{2}}{16} - \frac{y^{2}}{9} = 1

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 62

If the normal to the rectangular hyperbola

x y = 4

at the point

(2 t_{1}, \frac{2}{t_{1}})

meets the curve again at

(2 t_{2}, \frac{2}{t_{2}})

, then

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 63

If

4 x^{2} + p y^{2} = 45

and

x^{2} - 4 y^{2} = 5

cut orthogonally, then find the value of

p

.

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 64

Let

16 x^{2} - 3 y^{2} - 32 x - 12 y = 44

represents a hyperbola product of its square of eccentricity and length of latus rectum is

λ

then

3 \sqrt{3} λ

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 65

The focal distance of a point on the parabola

y^{2} = 16 x

whose ordinate is twice the abscissa is (except the vertex of parabola)

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 67

The minimum and maximum distance of a point

(\frac{9}{5}, \frac{12}{5})

from the ellipse

4 (3 x + 4 y)^{2} +

9 (4 x - 3 y)^{2} = 900

are

m

and

M

then the value of

m + M

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 69

The tangent at any point of a hyperbola

16 x^{2} - 25 y^{2} = 400

cut off a triangle from the asymptotes and that the portion of it intercepted between the asymptotes, then area of this triangle (in square units), is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 70

If

e_{1}

be the eccentricity of the conic

9 x^{2} + 4 y^{2} = 36

and

e_{2}

is the eccentricity of the conic

9 x^{2} - 4 y^{2} = 36

and

e_{3}

be the eccentricity of conic

x^{2} - y^{2} = 36

then

18 (e_{1}^{2} + e_{2}^{2}) \cdot e_{3}^{2}

is equal to -