Question

The equation $\frac{x^{2}}{12 - k} + \frac{y^{2}}{8 - k} = 1$ represents

• A. A hyperbola, if k < 8
• B. An ellipse, if k > 8
• C. A hyperbola, if 8 < k < 12
• D. None of these

Answer 1

Answer: (A)

A hyperbola, if k < 8

Answer 2

$\frac{\mathbf{x}^{\mathbf{2}}}{\mathbf{12}\mathbf{-}\mathbf{k}}\mathbf{+}\frac{\mathbf{y}^{\mathbf{2}}}{\mathbf{8}\mathbf{-}\mathbf{k}}\mathbf{= 1}$represents hyperbola, then 12 - k and 8 - k should be of opposite sign therefore 8 < k < 12 and will represent ellipse if both 12 - k and 8 - k are positive i.e. k < 8.