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

Answers (1)

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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