Question

If three normals can be drawn to the curve y2 = x from the point (c, 0), then find c.

Answer 1

We have y2 = x

⇒ dy/dx = 1/2y

Let the point P(t2, t) **** on the curve y2 = x

Equation of the normal to the curve at P is

y – t = –2t(x – t2)

which passes through the point (c, 0)

So, – t = – 2t(c – t2)

⇒ (c – t2) = 1/2

⇒ c – 1/2 = t 2

⇒ c – 1/2 > 0

⇒ c > 1/2

Hence, the value of c is c ∈u2009(1/2, ∞)