JEE-Advanced 2015 (24/40)

Geometry Level 3

Suppose that the foci of the ellipse x29+y25=1\frac{x^2}{9}+\frac{y^2}{5}=1 are (f1,0)(f_1,0) and (f2,0)(f_2,0) where f1>0f_1>0 and f2<0f_2<0. Let P1P_1 and P2P_2 be two parabolas with a common vertex at (0,0)(0,0) and with foci at (f1,0)(f_1,0) and (2f2,0)(2f_2,0) respectively. Let T1T_1 be a tangent to P1P_1 which passes through (2f2,0)(2f_2,0) and T2T_2 be a tangent to P2P_2 which passes through (f1,0)(f_1,0). If m1m_1 is the slope of T1T_1 and m2m_2 is the slope of T2T_2, then find the value of (1m12+m22)\left( \frac{1}{m_1^2}+m_2^2 \right)

×

Problem Loading...

Note Loading...

Set Loading...