Answer:
x =8 is the equation of the tangent.
Step-by-step explanation:
Here the equation of the given circle is: [tex](x-3)^{2} + (y+2)^{2} = 25[/tex]
Now, comparing it with the general equation of circle: [tex](x-h)^{2} + (y -k)^{2} = r^2[/tex]
we get the central coordinates (h,k) = (3,-2)
So, the slope of the line joining center and (8, -2) = [tex]\frac{-2 -(-2)}{8-3} = \frac{0}{5} = 0[/tex]
Since the slope of line = 0, line is parallel to x axis.
Now, as tangent and the line is perpendicular to each other
⇒Slope of the tangent = -1/ slope of the line = [tex]\frac{-1}{0}[/tex]
Now, by point slope formula: the equation of the tangent is
(y-y0) = m (x-x0)
or, [tex](y +2) = \frac{-1}{0} (x -8)[/tex]
or x =8 is the equation of the tangent.
