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. $x-y=1$

Answer 1

Answer: (B)

$x-y=0$

Answer 2

The correct answer is B:$x-y=0$
The equation of the given curve is $2y + x^2 = 3.$
Differentiating with respect to $x$, we have:
$2\frac{dy}{dx}+2x=0$
$=\frac{dy}{dx}=-x$
$=\frac{dy}{dx}\bigg]_{(1.1)}=-1$
The slope of the normal to the given curve at point (1, 1) is
$\frac{-1}{\frac{dy}{dx}\bigg]_{(1,1)}}=1.$
Hence, the equation of the normal to the given curve at (1, 1) is given as:
$y-1=1(x-1)$
$y-1=x-1$
$x-y=0$
The correct answer is B.