Question

Form the differential equation of:

All parabolas which have 4b as latus rectum and whose axis is parallel to Y-axis.

Answer 1

Let A(h, k) be the vertex of the parabola which has 4b as latus rectum and whose axis is parallel to the Y-axis.

Then equation of the parabola is

(x – h)² = 4b(y – k) ……. (1)

where h and k are arbitrary constants.

Differentiating both sides of (1) w.r.t. x, we get

Differentiating again w.r.t. x, we get

This is the required D.E.