Question

Find the locus of the point $(2a{\cos }^{2}t,2a\cos t)$, $t$ being parameter.

Answer 1

Let

$x=2a{\cos }^{2}t$

or, $\frac{x}{2a}={\cos }^{2}t$........(1)

And

$y=2a\cos t$

or, $\frac{y}{2a}=\cos t$.............(2).

Using the value of (2) in (1) we get,

$\frac{x}{2a}={\left(\frac{y}{2a}\right)}^2$

or, $y^2=2ax$.

So locus of the point is a parabola.