Question

What are represented by the equation $r{\sin }^2\theta =2a\cos \theta .$

Answer 1

$r{\sin }^2\theta =2a\cos \theta$

Using the parametric form $r\cos \theta =x,r\sin \theta =y,r=\sqrt{x^2+y^2}$

$r{\sin }^2\theta =2a\cos \theta r^2{\sin }^2\theta =2ar\cos \theta {\left(r\sin \theta \right)}^2=2ar\cos \theta y^2=2ax$

represnts a parabola with focus $(\frac{a}{2},0)$