If a, b and c form a geometric progression with common ratio r , then the sum of the ordinates of the points of intersection of the line a x+b y+c=0 and the curve x+2 y^2=0 is

Step-by-step solution

Since, a, b and c form a geometric progression a=a, b=a r, c=a r^2 Therefore, given line becomes aligned & a x+a r y+a r^2 & =0 & x+r y+r^2 & =0 & x & =-r y-r^2 aligned On putting x=-r y-r^2 in given curve x+2 y^2=0 , we get aligned -r y-r^2+2 y^2 & =0 2 y^2-r y-r^2 & =0 aligned Sum of ordinates = r 2