Question

How do I fins the slope of AB and the tangent line?

Answer 1

To represent the problem, we start from the following graph of the circle whose center is the point A(5,2).

The radius is indicated by the dotted line in the image that goes from point A to point B. The slope of radius AB is determine using the slope formula and taken that segment like an straight line.

The slope of radius AB is

`M_(AB)=(6-2)/(7-5)=(4)/(2)=2`

To calculate the slope of the tangent line, we assume that the tangent line is perpendicular to the radius line of the circle, so the slope of the tangent line will be

`M_T=-(1)/(M_(AB))=-(1)/(2)`

In other words,the slope of the tangent line is -1/2