### Home > PC > Chapter 8 > Lesson 8.1.4 > Problem8-60

8-60.

Find the equation of the line tangent to the circle $x^{2} + y^{2} = 25$ at the point $\left(3, 4\right)$. (Recall that a tangent line to a circle is perpendicular to that circle’s radius at the point of tangency.)

Draw a diagram of the situation.

Find the slope of the radius, AP.

Find the slope of the tangent line.

It is the negative reciprocal of the slope of the radius found above.

Now you have the point of tangency and the slope. Write the equation using the point-slope form.

$\frac{\text{rise}}{\text{run}}=\frac{4}{3}$

$(y-4)=-\frac{3}{4}(x-3)$