Question

The normal to the curve x² = 4y passing (1, 2) is

(A) x + y = 3 (B) x − y = 3

(C) x + y = 1 (D) x − y = 1

Answer 1

The equation of the given curve is x² = 4y.

Differentiating with respect to x, we have:

The slope of the normal to the given curve at point (h, k) is given by,

∴Equation of the normal at point (h, k) is given as:

Now, it is given that the normal passes through the point (1, 2).

Therefore, we have:

Since (h, k) lies on the curve x² = 4y, we have h² = 4k.

From equation (i), we have:

Hence, the equation of the normal is given as:

The correct answer is A.