If the vertex of the conic represented by 25x2+y2=(3x−4y+12)2 is (a,b) then the value of (b+a) is

25x2+y2=(3x−4y+12)2⇒x2+y2=3x−4y+125which is equation of the parabola having focus at A(0, 0) and directrixL≡3x−4y+12=0-----(i) Now equation of axis of the parabola is y=−43x or 4x+3y=0----(ii) Solving (i) and (ii), we get point B(−36/25,48/25) Now vertex is the mid point of AB , which is (−18/25,24/25) .