MathDB

Let

l,\ m

be the tangent lines passing through the point

A(a,\ a-1)

on the line

y=x-1

and touch the parabola

y=x^2

. Note that the slope of

l

is greater than that of

m

.
(1) Exress the slope of

l

in terms of

a

.
(2) Denote

P,\ Q

be the points of tangency of the lines

l,\ m

and the parabola

y=x^2

. Find the minimum area of the part bounded by the line segment

PQ

and the parabola

y=x^2

.
(3) Find the minimum distance between the parabola

y=x^2

and the line

y=x-1

Problem Statement