From point P(8,27) tangents P Q and P R are drawn to the ellipse x² 4 + y² 9 =1 . Then, angle subtended by Q R at origin is

Step-by-step solution

Equation of chord of contact Q R is aligned & 8 x 4 +27 y 9 =1 & 2 x+3 y=1 aligned Now, equation of the pair of lines passing through origin and points Q, R given by array l ( x² 4 + y² 9 )=(2 x+3 y)² 9 x²+4 y²=36 (4 x²+12 x y+9 y² ) 135 x²+432 x y+320 y²=0 array Required angle is array l = ⁻¹ 2 (216)²-135 320 455 = ⁻¹ 8 2916-2700 455 = ⁻¹ 8 216 455 = ⁻¹ 48 6 455 array