Question

The normal at the point (1, 1) on the curve 2 y + x 2 = 3 is (A) x + y = 0 (B) x − y = 0 (C) x + y + 1 = 0 (D) x − y = 1

Answer 1

The given equation of curve is,

2y+ x 2 =3

Differentiate the given equation with respect to x,

2 dy dx +2x=0 dy dx =−x

So, the slope of tangent at the point ( 1,1 ) is given as −1.

The slope of normal to the point ( 1,1 ) is,

−1 dy dx = −1 −1 =1

The equation of normal to the given curve at the given point is,

y−1=1( x−1 ) y−1=x−1 x=y x−y=0

Therefore, the correct option is (B).