An equilateral triangle whose two vertices are (-2,0) and (2,0) a… - Vidyadip

MCQ

An equilateral triangle whose two vertices are $(-2,0)$ and $(2,0)$ and which lies in the first and second quadrants only is circumscribed by a circle whose equation :-

A
$ \sqrt 3 x^2 + \sqrt 3y^2 - 4x - 4 \sqrt 3 = 0$
B
$\sqrt 3 x^2 + \sqrt 3 y^2 - 4x + 4 \sqrt 3 y = 0$
C
$\sqrt 3 x^2 + \sqrt 3 y^2 - 4y + 4 \sqrt 3 = 0$
✓
$\sqrt 3 x^2 + \sqrt 3 y^2 - 4y - 4 \sqrt 3 = 0$

✓

Answer

Correct option: D.

$\sqrt 3 x^2 + \sqrt 3 y^2 - 4y - 4 \sqrt 3 = 0$

d
Let $A \equiv(-2,0)$ and $B \equiv(2,0) .$ The centre of the circle is the centroid of the equilateral trinagle.

$\therefore $ $0 \equiv\left(0, \frac{2}{\sqrt{3}}\right)$ and $\mathrm{OA}=\frac{4}{\sqrt{3}}$

$\therefore $ Required circle is

$(x-0)^{2}+\left(y-\frac{2}{\sqrt{3}}\right)^{2}=\frac{16}{3}$

i.e. $\sqrt{3} x^{2}+\sqrt{3} y^{2}-4 y-4 \sqrt{3}=0$

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