JEE Main 2007 — Differential Equations Question with Solution
JEE Main 2007
Question
The differential equation of all circles passing through the origin and having their centres on the -axis is
Choose an option
Show full solutionCorrect option: C
Correct answer
C
Step-by-step explanation
General equation of all such circles is
.
Differentiating, we get
Desired equation is
$\begin{aligned}
& x^2+y^2+\left(-2 x-2 y \frac{d y}{d x}\right) x=0 \\
& \Rightarrow y^2=x^2+2 x y \frac{d y}{d x}.
\end{aligned}$
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This is a previous-year question from JEE Main 2007, covering the Differential Equations chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.