Q. If $x = h + a\sec\theta$ and$y = k + bcosec\ \theta$. Then,
A) $\frac{a^{2}}{(x + h)^{2}} - \frac{b^{2}}{(y + k)^{2}} = 1$
B) $\frac{a^{2}}{(x - h)^{2}} + \frac{b^{2}}{(y - k)^{2}} = 1$
C) $\frac{(x - h)^{2}}{a^{2}} + \frac{(y - k)^{2}}{b^{2}} = 1$
D) $\frac{(x - h)^{2}}{a^{2}\ } - \frac{(y - k)^{2}}{b^{2}} = 1$
Explanation
(b)
Given equations can be rewritten as
$\cos{\theta = \frac{a}{x - h},\ \ \sin{\theta = \frac{b}{y - k}}}$
Now, $\frac{a^{2}}{(x - h)^{2}}$+$\frac{b^{2}}{(y - k)^{2}} = 1\ \ \ \lbrack\because\cos^{2}{\theta + \sin^{2}{\theta = 1}}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.