If CP and CD be Any Two Semi-conjugate Diameters Of The Ellipse and The Circle With CP and CD as Diameters Intersect In R, Then R lies On The Curve

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

SPEAK TO COUNSELLOR ? CLICK HERE

Download JEE Question paper & Solution Download JEE Important questions Download Complete syllabus of Maths, Physics, Chemistry

Question

If CP and CD be any two semi-conjugate diameters of the ellipse and the circle with CP and CD as diameters intersect in R, then R lies on the curve

easy

Solution

Correct option is

2(x² + y²)² = a²x² + b²y²

C(0,0),

Equation of the circle with CP as diameter,

(x – x₁)(x – x₂) + (y – y₁)(y – y₂) = 0

… (1)

Similarly equation of circle with CD as diameter CD is

… (2)

Locus of point of int of (1) and (2) is obtained by elimination θ.

Download JEE Question paper & Solution Download JEE Important questions Download Complete syllabus of Maths, Physics, Chemistry

SIMILAR QUESTIONS

Q1

The area of the parallelogram formed by tangents at the extremities of two conjugate diameters of the ellipse is equal to

medium View solution

Q2

If the angle between the straight lines joining foci and the ends of minor axis of the ellipse is 90⁰ then the eccentricity is

easy View solution

Q3

The tangent and the normal to the ellipse x² + 4y² = 4 at a point P on it meet the major axis in Q and R respectively. If QR = 2, then the eccentric angle of P is

medium View solution

Q4

If CP and CD is a pair of semi-conjugate diameters of the ellipse,

, then CP² + CD² =

easy View solution

Q5

The line y = 2t² meets the ellipse in real point if

easy View solution

Q6

The locus of the foot of the perpendiculars to any tangent of an ellipse from the foci is

medium View solution

Q7

The product of the perpendiculars from the foci upon any tangent to the ellipse is

easy View solution

Q8

If P and D are the extremities of a pair of conjugate diameters of the ellipse , then the locus of the middle point ofPD is

easy View solution

Q9

The equation of the ellipse, referred to its axes as the axes of coordinates, which passes through the points (2, 2) and (1, 4) is

easy View solution

Q10

The locus of the point whose polar with respect to the ellipse touches the parabola y² = 4kx is

easy View solution