Question

The equation $r=5\cos \theta +12\sin \theta$ represents

• A. a circle
• B. an ellipse
• C. a parabola
• D. a straight line

Answer 1

Answer: (A)

a circle

Put $\cos \theta =\frac{x}{r}$ & $\sin \theta =\frac{y}{r}$ in $r=5\cos \theta +12\sin \theta$
where, $r=\sqrt{x^2+y^2}$
$r=\frac{5x}{r}+\frac{12y}{r}$
$\Rightarrow r^2=5x+12y$
$\Rightarrow x^2+y^2-5x-12y=0$
Therefore, given equation is circle.
Ans: A