Question

The point $(2\cos \theta ,3\sin \theta )$ lies ____________ the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$.

• A. outside
• B. inside
• C. on the periphery of
• D. on the auxillary of

Answer 1

The correct option is C on the periphery of

Given point is $(2\cos \theta ,3\sin \theta )$

Substituting given point in the ellipse equation:

$\frac{x^2}{4}+\frac{y^2}{9}-1$

$=\frac{4{\cos }^2\theta }{4}+\frac{9{\sin }^2\theta }{9}-1$

$={\cos }^2\theta +{\sin }^2\theta -1$

$=1-1=0$

$\therefore$ Given point satisfies the ellipse

$\Rightarrow$ point lie on periphery of ellipse.