Question

The equation of normal to the curve 2y=x² which passes through the point (2,1).

Answer 1

Answer :

Here, the curve is

2y = x² ...(i)

Now, differentiating both sides with respect to x, we get

2 dy/dx = 2x

⇒ dy/dx = x

⇒ - dx/dy = - 1/x

∴ (- dx/dy) at the point (2, 1) be

= - 1/2

∴ the required normal be

y - 1 = - 1/2 (x - 2)

⇒ 2 (y - 1) = - (x - 2)

⇒ 2y - 2 = - x + 2

⇒ x + 2y = 4

Hope it helps! (: