Question

The differential equation of family of circles whose centre lies on $x$ -axis, is

• A. $\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2+1=0$
• B. $y\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2-1=0$
• C. $y\frac{d^{2}y}{d{x}^2}-{\left(\frac{dy}{dx}\right)}^2-1=0$
• D. $y\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2+1=0$

Answer 1

Answer: (D)

The equation of family of circle having centre at
$x$ -axis is $x^2+y^2-2ax=0$
On differentiating, we get
$2x+2y\frac{dy}{dx}-2a=0$
Again, differentiating, we get
$2+2\left[y\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2\right]=0$
$\Rightarrow y\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2+1=0$