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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?

Solution Summary

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