If a, b, c form a G.P., then twice the sum of the ordinates of the points of intersection of the line ax + by + c = 0 and the curve x + 2y2 = 0 is

Let a, b, c be in G.P. with common ratio r.Then, b = ar and c = ar2.So, the equation of the line is ax + by + c = 0⇒ ax + ary + ar2 = 0 ⇒ x + ry + r2 = 0This line cuts the curve x + 2y2 = 0Eliminating x, we get 2y2 – ry + r2 = 0If the roots of the quadratic equation are y1 and y2, theny1+y2=r2⇒2y1+y2=r=ba=cb