9 5 x2 72 Suppose that the foci of the ellipse + = 1 are (f1,0) and (f2,0), where fi >0 and f<0. Let P, and P, be two parabolas with a common vertex at (0,0) with foci at 1,0) and (2f2,0), respectively. Let T be a tangent to P which passes through (2f2,0) and T, be a tangent to P2 which passes through (fi, 0). If my is the slope of T, and m, is the slope of T2, then the value of +,+ m2 is . ( 1 (2015 Adv.)

Suppose that the foci of the ellipse (x^2)/9+(y^2)/5=1 are (f_1,0)a n d(f_2,0) where f_1>0a n df_2<0. Let P_1a n dP_2 be two parabolas with a common vertex at (0, 0) and with foci at (f_1 .0)a n d (2f_2 , 0), respectively. LetT_1 be a tangent to P_1 which passes through (2f_2,0) and T_2 be a tangents to P_2 which passes through (f_1,0) . If m_1 is the slope of T_1 and m_2 is the slope of T_2, then the value of (1/(m1 2)+m2 2) is

Suppose that the foci of the ellipse (x^2)/9+(y^2)/5=1 are (f_1,0)a n d(f_2,0) where f_1>0a n df_2<0. Let P_1a n dP_2 be two parabolas with a common vertex at (0, 0) and with foci at (f_1 .0)a n d (2f_2 , 0), respectively. Let T_1 be a tangent to P_1 which passes through (2f_2,0) and T_2 be a tangents to P_2 which passes through (f_1,0) . If m_1 is the slope of T_1 and m_2 is the slope of T_2, then the value of (1/(m_1^ 2)+m_2^ 2) is

Suppose that the foci of the ellipse (x^2)/9+(y^2)/5=1 are (f_1,0)a n d(f_2,0) where f_1>0a n df_2<0. Let P_1a n dP_2 be two parabolas with a common vertex at (0, 0) and with foci at (f_1 .0)a n d (2f_2 , 0), respectively. Let T_1 be a tangent to P_1 which passes through (2f_2,0) and T_2 be a tangents to P_2 which passes through (f_1,0) . If m_1 is the slope of T_1 and m_2 is the slope of T_2, then the value of (1/(m_1^ 2)+m_2^ 2) is

Suppose that the foci of the ellipse (x^2)/9+(y^2)/5=1 are (f_1,0)a n d(f_2,0) where f_1>0a n df_2<0. Let P_1a n dP_2 be two parabolas with a common vertex at (0, 0) and with foci at (f_1 .0)a n d (2f_2 , 0), respectively. Let T_1 be a tangent to P_1 which passes through (2f_2,0) and T_2 be a tangents to P_2 which passes through (f_1,0) . If m_1 is the slope of T_1 and m_2 is the slope of T_2, then the value of (1/(m1 2)+m2 2) is

Suppose that the foci of the ellipse (x^2)/9+(y^2)/5=1 are (f_1,0)a n d(f_2,0) where f_1>0a n df_2<0. Let P_1a n dP_2 be two parabolas with a common vertex at (0, 0) and with foci at (f_1 .0)a n d (2f_2 , 0), respectively. Let T_1 be a tangent to P_1 which passes through (2f_2,0) and T_2 be a tangents to P_2 which passes through (f_1,0) . If m_1 is the slope of T_1 and m_2 is the slope of T_2, then the value of (1/(m_1^ 2)+m_2^ 2) is

Suppose that the foci of the ellipse (x^(2))/(9)+(y^(2))/(5)=1 are (f_(1),0) and (f_(2),0) where f_(1)gt0 and f_(2)lt0 Let P_(1) and P_(2) be two parabola with a c ommon vertex at (0, 0) and with foci at (f_(1),0) and (2f_(z),0) and T_(2) be a tangent to P_(2) which passes through (f_(1),0) . If m_(1) is the slope of T_(1) and m_(2) is the slope of T_(2) , then the value of ((1)/(m_(1)^(2))+m_(2)^(2)) , is

Suppose that the foci of the ellipse (x^(2))/(9)+(y^(2))/(5)=-1 are (f_(1),0) and (f_(2),0) where f_(1)gt0 and f_(2)lt0 . Let P_(1) and P_(2) be two parabolas with a common vertex at (0, 0) and with foci at (f_(1),0) and (2f_(2),0) respectively. Let T_(1) be a tangent to P_(1) which passes through (2f_(2),0) and T_(2) be a tangent to P_(2) which passes Through (f_(1),0) . If m_(1) is the slope of T_(1) and m_(2) is the slope of T_(2) , then the value of ((1)/(m_(1)^(2))+m_(2)^(2)) is -

F_(1) and F_(2) are the two foci of the ellipse (x^(2))/(9) + (y^(2))/(4) = 1. Let P be a point on the ellipse such that |PF_(1) | = 2|PF_(2)| , where F_(1) and F_(2) are the two foci of the ellipse . The area of triangle PF_(1)F_(2) is :