Question

$x^2+y^2-ax=0$ is represented by which of the following parametric equation?

• A. $(r\cos \theta -a)(r-a\cos \theta )=0.$
• B. $(r\cos \theta +a)(r+a\cos \theta )=0.$
• C. $(r\sin \theta -a)(r-a\sin \theta )=0.$
• D. None of these

Answer 1

The correct option is D None of these

Every point in (x,y) at a distance r from origin in the XY plane can be represented in the following way

$x=rcos\theta$

$y=rsin\theta$

Where $\theta$ is the angle made by the line joining origin and (x,y) with the positive X-axis.

Substituting x,y in the given equation

$(rcos\theta {)}^2+(rsin\theta {)}^2-a\left(rcos\theta \right)=0$

$r^2(co{s}^2\theta +si{n}^2\theta )-arcos\theta =0$

we know that $co{s}^2\theta +si{n}^2\theta =1$

$r^2-arcos\theta =0$

$r(r-acos\theta )=0$ is the parametric equation.