Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 51

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JEE Advanced

IMPORTANT

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The locus of the poles of the chords of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ subtending a right angle at its centre is

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Important Questions on Ellipse

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 52

The locus of the midpoints of the chords of the ellipse

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

whose poles are on the auxiliary circle on the tangents at the extremities of which intersect on the auxiliary circle, is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 53

If

C P

and

C D

are conjugate semi-diameters of the ellipse

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

, then, the locus of the midpoint of

P D

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 54

The locus of poles of tangents to the ellipse

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

with respect to concentric ellipse

\frac{x^{2}}{α^{2}} + \frac{y^{2}}{β^{2}} = 1,

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 55

The locus of pole of tangents to the ellipse

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

with respect to the parabola

y^{2} = 4 a x

, is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 56

The locus of the poles of normal chords of the ellipse

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

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 57

If

C P

and

C D

are conjugate semi-diameters of the ellipse, then

P D

touches the ellipse

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 58

If

α

and

β

are the angles subtended by the major axis of an ellipse at the extremities of a pair of conjugate diameters, then

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 59

If

P C P^{'}

and

D C D^{'}

form a pair of conjugate diameters of the ellipse

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

and

R

is any point on the circle

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

then