Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 2>Q 13

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IMPORTANT

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If the focal chord of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, (a > b)$ is normal at $(a \cos θ, bsin θ)$ then eccentricity of the ellipse is (it is given that $\sin θ \neq 0$ ).

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Important Questions on Ellipse

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 2>Q 14

P & Q

are corresponding points on the ellipse

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

, and the auxiliary circle respectively. The normal at

P

to the ellipse meets

C Q

in

R

where

C

is centre of the ellipse. Then

ℓ (C R)

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 2>Q 15

The locus of the foot of perpendicular drawn from the centre of the ellipse

x^{2} + 3 y^{2} = 6

on any tangent to it is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 3>Q 1

If

S

and

S^{'}

are the foci of the ellipse

\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1,

and

P

is any point on it, then range of values of

S P \cdot S^{'} P

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 3>Q 2

Let

P_{i}

and

{P_{i}}^{'}

be the feet of the perpendiculars drawn from foci

S,

S^{'}

on a tangent

T_{i}

to an ellipse whose length of semi-major axis is

20,

if

\sum_{i = 1}^{10} (S P_{i}) (S^{'} P_{i}^{'}) = 2560,

then the value of eccentricity is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 3>Q 3

The eccentricity of the curve represented by the equation

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

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 3>Q 4

Tangents are drawn to the ellipse

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

and the circle

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

at the points where a common ordinate cuts them (on the same side of the

x

-axis). Then the greatest acute angle between these tangents is given by

HARD

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 3>Q 5

The locus of point of intersection of two tangents of the ellipse

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

, meeting at right angles is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 3>Q 6

At a point

P

on the ellipse

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

tangent

P Q

is drawn. If the point

Q

be at a distance

\frac{1}{p}

from the point

P

, where

‘ p ’

is distance of the tangent from the origin, then the locus of the point

Q

is