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Question

Let the line 4x+3y+1=0 meets the parabola 8y2=ax at P,Q. If the angle made by chord PQ at the vertex of the parabola in 90°, then |a|=

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Solution

Given line
4x+3y+1=01=(4x+3y)
For the given parabola the vertex will be origin
Hence the pair of lines joinig the vertex to the intersection point of line and parabola will be
8y2=a(4x3y)x8y2+4ax2+3axy=0
For the pair of line to make right angle at origin
coefficient of x2+coefficient of y2=0a=2

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