Chapter 13.6, Problem 15PSB

To determine

To find: The point slope form, the equation of the tangent the circle at the point $\left(8,-8\right)$ .

Answer to Problem 15PSB

Therequired equation is $y+8=\frac{-5}{6}\left(x-8\right)$ .

Explanation of Solution

Given:

The equation of the circle is ${\left(x-2\right)}^2+{\left(y+3\right)}^2=61$ .

Calculation:

Consider the slope of the line from the centre to the point is calculated as,

  $\begin{array}{c}m=\frac{-8-\left(-3\right)}{8-2}\\ =\frac{-5}{6}\end{array}$

The slope of the tangent is $\frac{6}{5}$ .

Thus, the slope point form for the equation of the tangent to the given point is,

  $y+8=\frac{-5}{6}\left(x-8\right)$