If P x 1 , y 1 is a point on the hyperbola x 2 - y 2 = a 2 , then S P . S ' P = ________

Question

If P x 1 , y 1 is a point on the hyperbola x 2 - y 2 = a 2 , then S P . S ' P = ________, x 1 2 - y 1 2 a 2, x 1 2 + y 1 2 a 2, x 1 2 - y 1 2, x 1 2 + y 1 2

MARKS App · Accepted Answer

Given Hyperbola x 2 - y 2 = a 2 is Rectangular hyperbola, its e = 2 Then S 2 a , 0 and S ' - 2 a , 0 Also S ' P = 2 x 1 + a a n d S P = 2 x 1 - a Then S P S ' P = 2 x 1 2 - a 2 ∵ x 1 2 - y 1 2 = a 2 Hence, S P S ' P = x 1 2 + y 1 2

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