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

1) -r²/2

2) -r/2

3) r/2

4) r²/2

Solution:

Given a, b, c form a G.P. with a common ratio r.

So b = ar, c = ar²

Equation of line is ax + by + c = 0 ..(i)

Put b and c in (i)

ax + ary + ar² = 0

=> x = -r² – ry

Substitute the value of x in curve equation x + 2y² = 0

=> -r² – ry + 2y² = 0

=> 2y² – ry – r² = 0

=> y = r± √(r² + 8r²)/4 (using quadratic formula)

= 4r/4 or -2r/4

= r , -r/2

Sum of ordinates = r – r/2

= r/2

Hence option (3) is the answer.