Question

Choose the correct answer in the following question:

The normal at the point (1, 1) on the curve $2y+x^2=3$ is

(a) x + y = 0 (b) x - y = 0 (c) x + y + 1 = 0 (d) x - y + 1 = 0

Answer 1

The given curve is $2y+x^2=3$
On differentiating, we get $2\frac{dy}{dx}+2x=0\Rightarrow \frac{dy}{dx}=-x$
$\therefore$ Slope of normal at the given point $={\frac{-1}{\left(\frac{dy}{dx}\right)}}_{(1,1)}=\frac{-1}{-1}=1$
$\therefore$ Equation of the normal at (1, 1) is y - 1 = 1(X-1) or x - y = 0
Hence, the correct option is (b).