Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

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.

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