Q. The differential equation of the family of the curves $x^{2} + y^{2} - 2ax = 0$ is
A) $x^{2} - y^{2} - 2xy^{''} = 0$
B) $y^{2} - x^{2} = 2xyy'$
C) $x^{2} + y^{2} + 2y^{''} = 0$
D) None of these
Explanation
(b)
Given, $x^{2} + y^{2} - 2ax = 0$ …(i)
$\Rightarrow$ $2x + 2yy^{'} - 2a = 0$
$\Rightarrow$ $a = x + yy'$
On putting the value of $a$ in Eq. (i), we get
$x^{2} + y^{2} - 2x\left( x + yy^{'} \right) = 0$
$\Rightarrow$ $y^{2} - x^{2} = 2xyy'$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.