Question

The radius of the circle $r=12\cos \theta +5\sin \theta$ is

• A. $\frac{5}{12}$
• B. $\frac{17}{2}$
• C. $\frac{15}{2}$
• D. $\frac{13}{2}$

Answer 1

The correct option is D $\frac{13}{2}$

We have $r=12\cos \theta +5\sin \theta$

To convert above equation into Cartesian form

Substitute $\cos \theta =\frac{x}{r}$ and $\sin \theta =\frac{y}{r}$ and $r=\sqrt{x^2+y^2}$

$\Rightarrow r^2=12x+5y=x^2+y^2$

$\Rightarrow x^2+y^2-12x-5y=0$

Hence, radius $=\sqrt{{\left(\frac{12}{2}\right)}^2+{\left(\frac{5}{2}\right)}^2}=\frac{13}{2}$