If the circle (x-2√3)^2 + y^2 = 12 and parabola y^2 = 2√3x intersects at P, Q and R. Then the area of triangle PQR is

Question

If the circle \((x-2 \sqrt{3})^2+y^2=12\) and parabola \(y^2=2 \sqrt{3} x\) intersects at P, Q and R. Then the area of triangle PQR is

(1) 10 sq. units

(2) 12 sq. units

(3) 14 sq. units

(4) 16 sq. units

Answer 1

Correct option is (2) 12 sq. units  

Simply solving both we get \(x=0,2 \sqrt{3}\)

 

\(\triangle P Q R=\frac{1}{2} \times(4 \sqrt{3})(2 \sqrt{3})\)