JEE Main2004MathematicsParabolaActual

If a 0 and the line 2 b x+3 c y+4 d=0 passes through the points of intersection of the parabolas y^2=4 a x and x^2=4 a y , then

Options

Ad^2+(2 b+3 c)^2=0
Bd^2+(3 b+2 c)^2=0
Cd^2+(2 b-3 c)^2=0
Dd^2+(3 b-2 c)^2=0

Correct answer

A. d^2+(2 b+3 c)^2=0

Step-by-step solution

Points of intersection of given parabolas are (0,0) and (4 a, 4 a) equation of line passing through these points is y=x On comparing this line with the given line 2 b x+3 c y+4 d=0 , we get d=0 and 2 b+3 c=0 (2 b+3 c)^2+d^2=0

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