The Locus Of Pole Of Any Tangent To The Circle x2 + y2 = 4 W.r.t. The Hyperbola x2 – y2 = 4 Is The Circle

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

The locus of pole of any tangent to the circle x² + y² = 4 w.r.t. the hyperbola x² – y²= 4 is the circle

easy

Solution

Correct option is

x² + y² = 4

Any tangent to circle x² + y² = 4 is xx’, + yy’ = 4

or …. (1)

polar of a point (x₁, y₁) w.r.t. hyperbola x² – y²= 4 is

xx₁ – yy₁ = 4 …. (2)

by assumption (1) and (2) represent the same line.

Compare (1) & (2).

⇒ x₁² + y₁²= 4 ∴ locus is x² + y² = 4.

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

SIMILAR QUESTIONS

Q1

The locus rectum of the hyperbola

9x² – 16y² – 18x – 32y – 151 = 0 is

easy View solution

Q2

The eccentricity of the conjugate hyperbola of the hyperbola x² – 3y² = 1 is

easy View solution

Q3

The distance between the directrices of a rectangular hyperbola is 10 units, then distance between its foci is

easy View solution

Q4

The ,locus of the middle points of portions of the tangents to the hyperbola , intercepted between the axes is

easy View solution

Q5

If the polar of a point with respect to toches the hyperbola , then the locus of the point is

easy View solution

Q6

The foci of a hyperbola coincide with the foci of the ellipse . The equation of the hyperbola if its eccentricity is 2, is

easy View solution

Q7

The normal to the rectangular hyperbola xy = c² at the point ‘t’ meets the curve again at point “t” such that

medium View solution

Q8

PN is the ordinate of any point P on the hyperbola and AA’ is its transverse axis. If Q divides AP in the ratio a² : b², then NQ is

medium View solution

Q9

If SK perpendicular from focus S on th tangent at any point P of the hyperbola , then K lies on

easy View solution

Q10

The lines 2x + 3y + 4 = 0 and 3x – 2y + 5 = 0 may be conjugate w.r.t. the hyperbola if

medium View solution