Question

The cartesian equation of $r{\cos }^2\frac{\theta }{2}=a$ is

• A. $y^2=4ax$
• B. $x^2=4ay$
• C. $y^2=4a(x+a)$
• D. $y^2=4a(a-x)$

Answer 1

The correct option is D $y^2=4a(a-x)$

Given $r{\cos }^2\frac{\theta }{2}=a$
$r(1+\cos \theta )=2a$
$\Rightarrow r=2a-x$
$\Rightarrow r^2=4a^2+x^2-4ax$
$\Rightarrow y^2=4a(a-x)$