Question

State whether the following statement is true or false.

For all value of the coordinates of a moving point $P$ are $(acos\theta ,bsin\theta )$; then the equation to the locus of $P$ is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

• A. True
• B. False

Answer 1

The correct option is A True

Let $(x,y)$ be the co-ordinates of any point on the locus traced out by the moving point $P$. then we shall have ,

$x=acos\theta$

$\frac{x}{a}=cos\theta$

and $y=bsin\theta$

$\frac{y}{b}=sin\theta$

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=co{s}^2\theta +si{n}^2\theta$

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Which is the required equation to the locus of $P$.