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  4. If the segment intercepted by the parabola y = 4ax with the line lx + my + n = 0 subtends a right angle at the vertex, then

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Q. If the segment intercepted by the parabola $y = 4ax$ with the line $lx + my + n = 0$ subtends a right angle at the vertex, then

Conic Sections

Solution:

Make homogeneous and put $A + B = 0$
$y^2 = 4ax(\frac{lx + my}{-n})$
$\therefore 4al + n = 0$