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

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Question

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

Solution

Correct option is

x2 + y2 = 4

 

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

or                 …. (1)

polar of a point (x1y1) w.r.t. hyperbola x2 – y= 4 is

                xx1 – yy1 = 4                        …. (2)

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

Compare (1) & (2).

       

⇒ x12 + y1= 4        ∴ locus is x2 + y2 = 4.

Testing

SIMILAR QUESTIONS

Q1

 

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Q5

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Q6

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Q7

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Q8

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Q9

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Q10

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