# Math Help - Line Tangent to Two Parabolas

1. ## Line Tangent to Two Parabolas

The region r, is bounded by the graphs of f(x)=x^2-3, g(x)=(x-3)^2, and the line T. T is tangent to the graph of f at the point (a,a^2-3) and tangent to the graph of g at the point (b,(b-3)^2).

A) Show that a=b-3
B) Find the numerical value of a and b
C) write an equation of the line T

2. Originally Posted by rawkstar
The region r, is bounded by the graphs of f(x)=x^2-3, g(x)=(x-3)^2, and the line T. T is tangent to the graph of f at the point (a,a^2-3) and tangent to the graph of g at the point (b,(b-3)^2).

A) Show that a=b-3

$\color{red}\mbox{Since slope of T at first point = slope of T at 2nd one, you get } \,f'(a)=g'(b)$

B) Find the numerical value of a and b

$\color{red}\mbox{Find tangent line at 1st, 2nd points , compare both equations: they're the same!}$

Tonio

C) write an equation of the line T
.