Q. 125.0( 2 Votes )

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

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

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