Question

Find the differential equation of familyof parabolas having vertex at y axis and
axis of parabola is parallel to x-axis.​

Answer 1

Answer:

ANSWER

The equation of the family of parabolas having vertex at the origin and axis along positive y-axis is 

x2=4ay     (1), where a is a parameter.

Differentiating w.r.t. x, we get,

2x=4adxdy

a=2dxdyx

Substituting the value of a in equation 1, we get,

x2=4×2(dxdy)x×y

xdxdy=2y, which is the required differential equation.

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Answer 2

Answer:

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