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Q.
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 $b^{a} r^{a}=$
TS EAMCET 2020
Solution:
A circle is passing through $(3,4),(3,2)$ and $(1,4 C(1,4) \ldots B(3,4)$
Clearly, $\triangle A B C$ is a right angle triangle
- centre of circle is mid-point of $A C$ i.e., $O(2,3)$
$r=A O=\sqrt{(3-2)^{2}+(2-3)^{2}}=\sqrt{1+1}=\sqrt{2}$
Equation of circle in parameter form is
$x=2+\sqrt{2} \cos \theta$
$\Rightarrow y=3+\sqrt{2} \sin \theta$
$\therefore a=2, b=3, r=\sqrt{2}$
$b^{a} \cdot r^{a}=(3)^{2}(\sqrt{2})^{2}=9 \times 2=18$
