Question

Let $P = \left(\frac{15}{2}(\csc \theta + \sin \theta), \; 8(\csc \theta - \sin \theta)\right)$, where $\theta$ is a variable parameter. Then the locus of $P$ is

• A. $\frac{x^2}{15} - \frac{y^2}{16} = 1$
• B. $\frac{x^2}{256} - \frac{y^2}{225} = 1$
• C. $\frac{x^2}{225} + \frac{y^2}{256} = 1$
• D. $\frac{x^2}{225} - \frac{y^2}{256} = 1$
• E. $\frac{x^2}{16} + \frac{y^2}{30} = 1$

Hint:

Convert parametric trig forms into algebraic form using identities like $a^2-b^2$.

Answer 1

The Correct Option is D