Chapter 11.6, Problem 94AYU

To determine

To find:The equation of tangent line to the parabola $y+x^2-5=0$ at point $\left(-2,-2\right)$

Answer to Problem 94AYU

The equation of tangent is $y=4x+9$ .

Explanation of Solution

The equation of line is $y=mx+b$ .

  $\begin{array}{c}2m-b+1=0\\ b=2m+1\end{array}$

The equation of tangent is,

  $y=2m+mx+1$

So,

  $\begin{array}{c}y+x^2-5=0\\ 2m+mx+x^2-4=0\end{array}$

The determinant of the quadratic equation is,

  $\begin{array}{c}{m}^2-8m+16=0\\ m=4\end{array}$

Thus, the equation of tangent is,

  $y=4x+9$

Therefore, the equation of tangent is $y=4x+9$ .