Question

The differential equation of the family of circles passing through the fixed points $(a, 0)$ and $(-a, 0)$ is

• A. $y_{1}\left(y^{2}-x^{2}\right)+2xy +a^{2}=0$
• B. $y_{1}y^{2}+xy +a^{2}x^{2} = 0$
• C. $y_{1}\left(y^{2}-x^{2}+a^{2}\right)+2xy = 0$
• D. $y_{1}\left(y^{2}+x^{2}\right)-2xy +a^{2}= 0$

Answer 1

Answer: (C)

$y_{1}\left(y^{2}-x^{2}+a^{2}\right)+2xy = 0$

Answer 2

Let the equation of circle passing through given points is