Question

Please help. 10 points. Please do not guess. Guesses will be reported. Thank you. :)

Answer 1

a. The radius is the distance from the circle's center to the point of tangency:

`√((10-6)^2+(5-(-3))^2)=√(80)=4\sqrt5`

b. The line tangent to the circle is perpendicular to the line connecting points A and B. Lines perpendicular to one another have slopes that are negative reciprocals of one another. In other words, if the slope of the line through A and B is
`m`, then the slope of the tangent line is
`-\frac1m`.

Find the slope of the line through A and B:

`m=(10-6)/(5-(-3))=\frac12\implies-\frac1m=-2`