The normal at the point (1, 1) on the curve 2y + x² = 3 is
(A) x + y = 0  (B) x - y = 0  (C) x + y + 1 = 0  (D) x - y = 1

Solution:

The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line.

The equation of the given curve is

2y + x² = 3

Differentiating with respect to x ,

we have:

2 dy/dx + 2x = 0

dy/dx = - x

dy/dx]_{(1, 1)} = - 1

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

(- 1)/dy/dx]_{(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

Thus, the correct option is B

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise ME Question 22

The normal at the point (1, 1) on the curve 2y + x² = 3 is (A) x + y = 0 (B) x - y = 0 (C) x + y + 1 = 0 (D) x - y = 1

Summary:

The normal at the point (1, 1) on the curve 2y + x² = 3 is x - y = 0. Thus, the correct option is B