Question

What normal to the curve y = x2 forms the shortest chord?

Answer 1

Given curve is y = x2

Let A = (t, t2)

Equation of the tangent at A = (t, t2) is

y – t2 = ( – 1/2t)(x – t)

Let the normal intersects the curve again at B

where B = (t1, t12)

So L is minimum.

Thus, the equation of AB is