Question

If \(a\neq 0\) and the line \[ 2bx+3cy+4d=0 \] passes through the points of intersection of the parabolas \[ y^2=4ax \] and \[ x^2=4ay, \] then

• A. \[ d^2+(2b-3c)^2=0 \]
• B. \[ d^2+(3b+2c)^2=0 \]
• C. \[ d^2+(2b+3c)^2=0 \]
• D. \[ d^2+(3b-2c)^2=0 \]

Hint:

When a line passes through the intersection points of two curves, first determine the common points by solving the equations simultaneously. Then substitute those points into the line equation to obtain the required relation among the parameters.

Answer 1

The Correct Option is C