# 22) 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

G Gautam harsolia

Given the equation of the curve
$2y + x ^2 = 3$
We know that the slope of the tangent at a point on the given curve is given by  $\frac{dy}{dx}$
$2\frac{dy}{dx} = -2x\\ \frac{dy}{dx} = -x$
We know that
$Slope \ of \ normal = \frac{-1}{Slope \ of \ tangent } = \frac{-1}{-x} = \frac{1}{x}$
At point (1,1)
$Slope = \frac{1}{1} = 1$
Now, the equation of normal with point (1,1) and slope = 1

$y-y_1=m(x-x_1)\\ y-1=1(x-1)\\ x-y = 0$
Hence, the correct answer is (B)

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