If the line y = x + c touches the hyperbola x 2 9 - y 2 5 = 1 at the point P h , k , then h , k can be equal to

Question

If the line y = x + c touches the hyperbola x 2 9 - y 2 5 = 1 at the point P h , k , then h , k can be equal to, 9 2 , - 5 2, 9 2 , 5 2, - 5 2 , - 9 2, 5 2 , - 9 2

MARKS App · Accepted Answer

Tangent at P h , k is h x 9 - k y 5 = 1 which is same as y = x + c (where c = ± 9 1 - 5 = ± 2 ) ⇒ h x 9 - k y 5 - 1 = 0 and x - y ± 2 = 0 are identical ⇒ h 9 1 = - k 5 - 1 = - 1 ± 2 ⇒ h , k = - 9 2 , - 5 2 o r 9 2 , 5 2

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