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Question: variable curves C<sub>1</sub> : y<sup>2</sup> = 4a(x – b<sub>1</sub>) and C<sub>2</sub>: x<sup>2</su...

variable curves C1 : y2 = 4a(x – b1) and C2: x2 = 4a

(y – b2) where 'a' is a given positive real number and b1 and b2 are variables, touch each other. Locus of the point of contact is

A

xy = a2

B

xy = 2a2

C

xy = 4a2

D

None

Answer

xy = 4a2

Explanation

Solution

Let P(x, y) be the point of contact. Slope of the curves at the point of contact are and . Thus 2ay=x2a\frac { 2 a } { y } = \frac { x } { 2 a }

⇒ xy = 4a2.