Question
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
⇒ 2a = 22c ⇒ a2 = 2c2