Hyperbola Question - None

Question

Point of hyperbola \left(ct, \frac{c}{t}\right)\ lie on director circle x^2 + y^2 = a^2 + b^2\ of ellipse

Accepted Answer

Solution:

For the point \left(ct, \frac{c}{t}\right)\ to lie on the director circle:

c^2t^2 + \frac{c^2}{t^2} = a^2 + b^2\

Since c^2\left(t^2 + \frac{1}{t^2}\right) \geq 2c^2\ (by AM-GM inequality)

We need a^2 + b^2 \geq 2c^2\

But for a hyperbola, c^2 = a^2 + b^2\, so a^2 + b^2 < 2c^2\

This is impossible. ∴ Answer is (a)

Question: