# Form the differential equation of all parabolas whose axis is the X-axis. - Mathematics and Statistics

Sum

Form the differential equation of all parabolas whose axis is the X-axis.

#### Solution

The equation of the parbola whose axis is the X-axis is y2 = 4a(x - h),     ....(1)

where a and h are arbitrary constants.

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

"2y"("dy"/"dx") = 4"a"(1 - 0)

∴ y"dy"/"dx" = "2a"

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

"y" * "d"/"dx"("dy"/"dx") + "dy"/"dx" * "dy"/"dx" = 0

∴ "y"("d"^2"y")/"dx"^2 + ("dy"/"dx")^2 = 0

This is the required D.E.

Concept: Formation of Differential Equations
Is there an error in this question or solution?