Question

The differential equation for all the straight lines which are at a unit distance from the origin is

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

Answer 1

Answer: (C)

Let equation of St. Line
$Y-y=m(X-x)$
Distance from origin $\Rightarrow\left|\frac{ mx - y }{\sqrt{1+ m ^2}}\right|=1$
$\therefore (m x-y)^2=1+m^2$
$ \left(y-\frac{d y}{d x} x\right)^2=1+\left(\frac{d y}{d x}\right)^2$