The differential equation satisfied by the system of parabolas y^2=4a(x+a) is:

Question

Accepted Answer

Correct answer: C. (c) JEE Main 2021 y^2=4 ax+4a^2 Differentiate with respect to x ⇒2y dy dx=4a ⇒a= ( y2 dy dx ) So, required differential equation is y^2=(4 y2 dy dx)x+4 ( y2 dy dx )^2 ⇒y^2 ( dy dx )^2+2 xy ( dy dx )-y^2=0 ⇒y ( dy dx )^2+2x ( dy dx )-y=0

$The differential equation satisfied by the system of parabolas y^{2} = 4 a (x + a) is:$

Solution

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