From a point P(8,27) tangents PQ and PR are drawn to the ellipse x²/4+y²/9=1. Then the angle subtended by QR at the origin is___________?

Try it, its really a good problem.

let tangent be (y-27)/(x-8)=m,

y=m(x-8)+27, equation(1)

(x^2/4)+(((m(x-8)+27))^2/9)=1,equation(2)

 this is a quadratic equation in 'x'. for a tangent, there should be only one root, implying that discriminant is zero. From this condition you will get a quadratic equation in 'm'. solve it to obtain the two values of 'm' and using (1) and (2), find the coordinates of Q and R, and then youcan easily obtain the answer

Approved

@chetan, you missed the concept. The problem was given with the intention to use homogenization concept. Try to solve the problem by homogenization.