Let P ( h , k ) be the point of contact of the tangent to the hyperbola 5 x^2-7 y^2-35=0 which is parallel to the line 2 x-y+ =0 . If P lies in the third quadrant then 3 h^2-2 k=

Step-by-step solution

The given eqn. of hyperbola is 5 x^2-7 y^2-35=0 ...(i) Differentiating (i), we get 10 x-14 y y^ =0 y^ = 5 x 7 y (y^ )_ (h, k) = 5 h 7 k Tangent line is parallel to 2 x-y+ =0 y^ = 2 5 h 7 k = 2 25 h^2 49 k^2 =2 Point P also lies on 5 x^2-7 y^2-35=0 5 h^2-7 k^2-35=0 2 49 k^2 5 -7 k^2-35=0 aligned & 25 h^2=2 49 25 9 h^2= 98 9 & 3 h^2-2 k=3 98 9 +2 5 3 = 98+10 3 & 3 h^2-2 k= 108 3 =36 . aligned