Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 79

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IMPORTANT

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If $θ$ and $ϕ$ are eccentric angle of the ends of a pair of conjugate diameters of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ , then $θ - ϕ$ is equal to

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Important Questions on Conic Section

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IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 80

If

r_{1}

and

r_{2}

are the focal distances of the point at which normal is drawn to the curve

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

then the portion of normal intercepted between curve and the major axis is

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 81

The number of real tangents through

(3, 5)

to

3 x^{2} + 5 y^{2} = 32,

is/ are

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 82

The locus of point of intersection of tangents to an ellipse at two points, the sum of whose eccentric angles is constant, is

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 83

The eccentricity of the ellipse which meets the straight line

\frac{x}{7} + \frac{y}{2} = 1

on the axis of

x

and the straight line

\frac{x}{3} - \frac{y}{5} = 1

on the axis of

y

and whose axes lie along the axes of co-ordinate, is -

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 84

The number of normals that can be drawn from a point to a given ellipse is

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 87

The equations of the tangents to the ellipse

4 x^{2} + 3 y^{2} = 5,

which are inclined at

60 °

to the

x

-axis are

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 88

If the tangent and normal to

x y = c^{2}

at a given point on it cut off intercepts

a_{1}, a_{2}

on one axis and

b_{1}, b_{2}

on the other axis, then

a_{1} a_{2} + b_{1} b_{2} =

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 89

The foci of hyperbola

x y = (\frac{a^{2} + b^{2}}{4})

are given by