Question
Find the equation of the parabola whose focus is at point S (2, 5) and the directrix is line 3x + 4y + 1 = 0.
Solution
Let line l be the directrix with equation
3x + 4y + 1 = 0 and S (2, 5) be the focus.
Take a point on the parabola
∴ By definition, PS = 'PM d = p
Hence, the locus of P or the equation of parabola is :