Circle 3 Question 15
15. The equation of circle $C$ is
(a) $(x-2 \sqrt{3})^{2}+(y-1)^{2}=1$
(b) $(x-2 \sqrt{3})^{2}+y+\frac{1}{2}^{2}=1$
(c) $(x-\sqrt{3})^{2}+(y+1)^{2}=1$
(d) $(x-\sqrt{3})^{2}+(y-1)^{2}=1$
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Answer:
Correct Answer: 15. (d)
Solution:
- Let centre of circle $C$ be $(h, k)$.
$$ \begin{aligned} & \text { Then, } \\ & \left|\frac{\sqrt{3} h+k-6}{\sqrt{3+1}}\right|=1 \\ & \begin{array}{lc} \Rightarrow & \sqrt{3} h+k-6=2,-2 \\ \Rightarrow & \sqrt{3} h+k=4 \end{array} \end{aligned} $$
[rejecting 2 because origin and centre of $C$ are on the same side of $PQ$ ] The point $(\sqrt{3}, 1)$ satisfies Eq. (i).
$\therefore \quad$ Equation of circle $C$ is $(x-\sqrt{3})^{2}+(y-1)^{2}=1$.
Clearly, points $E$ and $F$ satisfy the equations given in option (d).
