Question

If $P(a \cos \theta, b \sin \theta)$ is a point on an ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$, then ' $\theta$ ' is

• A. angle of $O P$ line from positive direction of $x$-axis ( $O$ is origin)
• B. angle of $O Q$ line from positive direction of $x$-axis [when $Q$ is $(a \cos \theta, a \sin \theta)$ ]
• C. it depends on the pont $P$
• D. none of the above

Answer 1

Answer: (B)

$P(a \cos \theta, b \sin \theta)$, then $\theta$ is angle of a corresponding pont on auxilliary circle $x^{2}+y^{2}=a^{2}$ i.e., $(a \cos \theta, a$ $\sin \theta)$