If the equation 3 x^2+7 x y+2 y^2+2 g x+2 f y+2=0 represents a pair of intersecting lines and the square of the distance of their point of intersection from the origin is 2 5 , then f^2+g^2=

Step-by-step solution

The equation, represents a pair of intersecting lines, so aligned & (3) (2)(2)+7(g)(f)-3 f^2-2 g^2-2 ( 7 2 )^2=0 & 24+14 g f-6 f^2-4 g^2-49=0 aligned To get the point of intersection of pair of straight lines, we have to differentiate partially the Eq. (i) with respect to x and y respectively. then we are getting Now, point of intersection of eqs. (iii) and (iv) is the point of intersection of pair of straight line Eq. (i). ( 14 f-8 g 25 , 14 g-12 f 25 ) Now, according to the question, aligned & ( 14 f-8 g 25 )^2+