Chapter 11.6, Problem 91AYU

To determine

To Solve: The equation $m^2-4(2m - 4) = 0$ and to write equation of tangent line.

Answer to Problem 91AYU

Solution:

$m = 4,y = 4x - 4$

Explanation of Solution

Given:

$\begin{array}{l}y = x^2\\ y = mx + 4 - 2m\end{array}$

And $(2,4)$ to be the unique solution to the system.

Calculation:

$\begin{array}{rrr}\hfill m^2 - 4(2m - 4)& \hfill = & 0\hfill \\ \hfill m^2 - 8m + 16& \hfill = & 0\hfill \\ \hfill m& \hfill = & \hfill 4,4\end{array}$

Equation of tangent line is $y = mx + b$

Here $b = 4 - 2m = - 4$

Therefore, $y = 4x - 4$