2017HyperbolaHard

Question

If 2x - y + 1 = 0 is a tangent to the hyperbola x2a2-y216=1, then which of the following CANNOT be sides of a right angled triangle ?

Options

A.

2a, 4, 1

B.

2a, 8, 1

C.

a, 4, 1

D.

a, 4, 2

Solution

Tangent to x2a2-y242=1 is

y =mx ±a2m2-16

Comparing with y = 2x + 1

m = 2

⇒4a2 - 16 = 1

a2 =  174

a = 172

Only 2a, 4, 1 are sides of a right-angled triangle

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