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

The Correct Option is B

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.