Question

If the parametric equations of the circle passing through the points $(3,4),(3,2)$ and $(1,4)$ is $x=a+r\cos \theta ,y=b+r\sin \theta$, then $b^a{r}^a=$

• A. 27
• B. 18
• C. 9
• D. 54

Answer 1

Answer: (B)

A circle is passing through $(3,4),(3,2)$ and $(1,4C(1,4)\dots B(3,4)$

Clearly, $△ABC$ is a right angle triangle
- centre of circle is mid-point of $AC$ i.e., $O(2,3)$
$r=AO=\sqrt{(3-2{)}^2+(2-3{)}^2}=\sqrt{1+1}=\sqrt{2}$
Equation of circle in parameter form is
$x=2+\sqrt{2}\cos \theta$
$\Rightarrow y=3+\sqrt{2}\sin \theta$
$\therefore a=2,b=3,r=\sqrt{2}$
$b^a\cdot r^a=(3{)}^2(\sqrt{2}{)}^2=9\times 2=18$