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

Answer: (D)

Given equation of circle is
$r=12 \cos \theta+5 \sin \theta$
Put $\cos \theta=\frac{x}{r}$ and $\sin \theta=\frac{y}{r}$, we get
$r =12 \times \frac{x}{r}+5 \times \frac{y}{r} $
$\Rightarrow r^{2} =12 \,x+5\, y$
$\Rightarrow x^{2}+y^{2}=12 x+5 y$
$\Rightarrow x^{2}+y^{2}-12 x-5 y=0$
$\therefore $ Centre is $\left(6, \frac{5}{2}\right)$.
$ \therefore \text { Radius of circle } =\sqrt{(6)^{2}+\left(\frac{5}{2}\right)^{2}} $
$=\sqrt{36+\frac{25}{4}}=\sqrt{\frac{144+25}{4}} $
$=\sqrt{\frac{169}{4}}=\frac{13}{2} $