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 = 0
This line cuts the curve x + 2y2 = 0
Eliminating x, we get 2y2 – ry + r2 = 0
If the roots of the quadratic equation are y1 and y2, then