Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-1>Q 15

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$P Q$ is a double ordinate of the ellipse $x^{2} + 9 y^{2} = 9$ , the normal at $P$ meets the diameter through $Q$ at $R,$ then the locus of the mid point of $P R$ is -

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Important Questions on Ellipse

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-1>Q 16

The equation of the chord of the ellipse

2 x^{2} + 5 y^{2} = 20

which is bisected at the point

(2, 1)

is

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-1>Q 17

If

F_{1} & F_{2}

are the feet of the perpendiculars from the foci

S_{1} & S_{2}

of an ellipse

\frac{x^{2}}{5} + \frac{y^{2}}{3} = 1

on the tangent at any point

P

on the ellipse, then

(S_{1} F_{1}) \cdot (S_{2} F_{2})

is equal to-

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-1>Q 18

If

\tan θ_{1} \cdot \tan θ_{2} = - \frac{a^{2}}{b^{2}}

then the chord joining two points

θ_{1} & θ_{2}

on the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

will subtend a right angle at

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-1>Q 19

The number of values of

c

such that the straight line

y = 4 x + c

touches the curve

(\frac{x^{2}}{4}) + y^{2} = 1

is -

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-2>Q 1

If a real circle will pass through the points of intersection of hyperbola

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

and parabola

y = x^{2}

, then-

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-2>Q 2

x - 2 y + 4 = 0

is a common tangent to

y^{2} = 4 x & \frac{x^{2}}{4} + \frac{y^{2}}{b^{2}} = 1 .

Then the value of

' b'

and the other common tangent are given by

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-2>Q 3

The tangent at any point

P

on a standard ellipse with foci as

S

and

S^{'}

meets the tangents at the vertices

A

and

A'

in the points

V

and

V'

, then -

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Beta Question Bank for Engineering: Mathematics>Chapter 19 - Ellipse>EXERCISE-2>Q 4

The area of the rectangle formed by the perpendiculars from the centre of the standard ellipse to the tangent and normal at its point whose eccentric angle is

\frac{π}{4}

is -