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Question: If hyperbola x<sup>2</sup> - y<sup>2</sup> = a<sup>2</sup> and xy = c<sup>2</sup> are of same size, ...

If hyperbola x2 - y2 = a2 and xy = c2 are of same size, then:

A

c2 = 2a2

B

c = 2a

C

2c2 = a2

D

None of these

Answer

2c2 = a2

Explanation

Solution

Distance between their vertices will remain same (length of transverse axis) 2a is distance between vertices is Ist hyperbola (c, c) and (-c, -c) are vertices of 2nd.

2a = (c+c)2+(c+c)2\sqrt{(c + c)^{2} + (c + c)^{2}}

⇒ 2a = 22\sqrt{2}c ⇒ a2 = 2c2