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JEE MainMathematicsModerateDifferential equation

The differential equation representing the family of ellipses
having foci either on the x-axis or on the y-axis, centre at the origin
and passing through the point (0, 3) is:
ij fcUnq (0, 3)

Show answer and solution
Equation of ellipse
nh?kZ o`Ùk dk lehdj.k
x2a2+y2b2=1\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1
Passes (0, 3) ls xqtjrk
⇒\Rightarrow x2a2+y29=1\frac{x^{2}}{a^{2}} + \frac{y^{2}}{9} = 1......(1)
xa2=−y9dydx\frac{x}{a^{2}} = - \frac{y}{9}\frac{dy}{dx}
2xa2+2y9dydx=0\frac{2x}{a^{2}} + \frac{2y}{9}\frac{dy}{dx} = 0......(2)
1a2=−y9xy′\frac{1}{a^{2}} = - \frac{y}{9x}y^{'}
By lehdj.k (1) &o (2) ls equation is
−xy9y′+y29=1- \frac{xy}{9}y^{'} + \frac{y^{2}}{9} = 1
⇒\Rightarrow xy y' - y^2 + 9 = 0

Source: Grass-G / M-21 Mathematics Paper 19 Dec Hindi Eng.docx

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