If the equation 3x2+7xy+2y2+2gx+2fy+2=0 represents a pair of intersecting lines and the square of the distance of their point of intersection from the origin is
The equation, 3x2+7xy+2y2+2gx+2fy+2=0 Above equations shows the pair of intersecting lines, so1 (3)(2)2+7gf−3f2−2g2−49=0 24+114gf−6f2−4g2−49=0 4g2+6f2−14gf+25=0 To get point of interaction of pair of straight line the equation should be differentiate with respect to x and y . So, 6x+7y+2g=0 …… (I) 7x+4y+2f=0 …… (II) Now, point of interaction of line (I) and (II) is, (