# Gradient and equation of tangent

Say I have for example a circle with centre C(7,-5) passing through point A(6,-3)

(With tangent line and radius, AC, being perpendicular.)

1. How would I go about finding the gradient of the tangent?

2. How would I go about finding that the equation of the tangent at A is the line x=2y+12 ?

3. And how would I go about finding out that this line meets a second circle with

equation of x squared -24x +y squared +10y +149=0 in only one point?

https://brainmass.com/math/graphs-and-functions/gradient-equation-tangent-57054

#### Solution Preview

Please see the attached file.

Say I have for example a circle with centre C(7,-5) passing through point A(6,-3)

(With tangent line and radius, AC, being perpendicular.)

1. How would I go about finding the gradient of the tangent?

First, we can compute the slope of the line CA, denoted by k,

So, the slope of the ...

#### Solution Summary

This shows how to find gradient and equation of a tangent to a circle.