HOW to derive the relation for a tangent having equation Ax+By+C=0 intersecting with a parabola y²=4ax ??

Dear Student:

A line will be a tangent to a parabola iff on solving two equations we should get one and only one solution.

So solve the two equations – Ax + By + C = 0 and y2 = 4ax – convert them in any one variable (x or y) then after getting the quadratic in x or y apply the condition D = 0 i.e. discrimenent = 0.

Best of Luck!