Question

The equation, $r{\sin }^2\theta =2a\cos \theta$ Represents which of the following curve?

• A. Parabola
• B. Hyperbola
• C. Ellipse
• D. Circle

Answer 1

The correct option is A Parabola

It is given that, $r{\sin }^2\theta =2a\cos \theta$

Now, in parametric form $\sin \theta =\frac{y}{r}$ and $\cos \theta =\frac{x}{r}$

Substituting the value of $\sin \theta$ and $\cos \theta$ in the original equation we have,

$r\times (\frac{y}{r}{)}^2=2a\times (\frac{x}{r})$

$\Rightarrow y^2=2ax$

This is the equation of a Parabola.