The pole of a non-horizontal line lx + my + n = 0 w.r.t. y2 = 4ax is
Proof : Let the pole of a non-horizontal line lx + my + n = 0 (l ≠ 0) .... (1)
w.r.t. the parabola y2 = 4ax be P(x1, y1) .... (2)
Then the equation of the polar of P w.r.t. S = 0 is yy1 = 2a(x + x1) or 2ax – yy1 + 2ax1 = 0 .... (3)
Since (1) and (3) represents the same line, we have
= =
⇒ x1 = , y1 =
∴ The pole of (1) w.r.t. S = 0 is .