JEE Main On 16 April 2018 Question 12
Question: The differential equation representing the family of ellipse having foci either on the x-axis or on the y-axis, centre at the origin and passing through the point $ (0,3) $ is?
Options:
A) $ xyy’+y^{2}-9=0 $
B) $ x+y{y^{’’}}=0 $
C) $ xyy’’+x{{(y’)}^{2}}-yy’=0 $
D) $ xyy’-y^{2}+9=0 $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 $
it passes through (0,3), so it will become $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{9}=1 $
different w.r.t x, we get $ \frac{2x}{a^{2}}+\frac{2y}{9}\frac{dy}{dx}=0 $
$ \frac{y}{x}( \frac{dy}{dx} )=\frac{-9}{a^{2}} $
diff w.r.t x, we get $ (\frac{y}{x}\frac{d^{2}y}{dx^{2}})+\frac{x\frac{dy}{dx}-y}{x^{2}}\frac{dy}{dx}=0 $ $ xyy’’+xy{{’}^{2}}-yy’=0 $
