Question

Form the differential equation that represents all parabolas each of which has a latus rectum 4a and whose axes are parallel to the x-axis.

Answer 1

Equation of parabola whose axis is parallel to the x-axis with latus rectum 4a is 

(y – β)² = 4a(x – α) ………(1) 

Here (α, β) is the vertex of the parabola. 

Differentiating (1) w.r.t x, we get 

2(y – β)dy/dx = 4a ……. (2) 

Again, differentiating (2) w.r.t x, we get