Question

The centre of the circle passing through $(1,\sqrt{3})$ , $(1,-3)$, $(3,-\sqrt{3})$ is

• A. $(2,0)$
• B. $(-2,0)$
• C. $(-2,2)$
• D. $(2,-2)$

Answer 1

The correct option is A $(2,0)$

Point A: $A(1,\sqrt{3}),B(1,-\sqrt{3})$ and $C(1,-\sqrt{3})$ lie on circle.
And $<ABC={90}^0$
So, circle having $C(3,-\sqrt{3})$ and $A(1,\sqrt{3})$ as diametric ends is given by.
$(x-3)(x-1)+(y+\sqrt{3})(y-\sqrt{3})=0$
$\Rightarrow x-4x+3+y^2-3=0$
$\Rightarrow x^2+y^2-4x=0$
So, centre of circle is $(2,0).$