Find the differential equation of all the parabolas with latus rectum ‘4a' and whose axes are parallel to the x - axis.

Question

Philoid · Accepted Answer

Equation of parabola with latus rectum ‘4a’ and axes parallel to x - axes and vertex at (h,k) is given by

(y – k)² = 4a(x – h)

On differentiating with respect to x we get,

Again differentiating (i) with respect to x we get,

From (i) we have , on substituting it in the above equation we get,

Hence, the required differential equation is