Question

Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the equation of the line containing the points of tangency.

Answer 1

`y=-x+r`

Explanation:

we know that

The tangency point on the x-axis is (r,0)

The tangency point on the y-axis is (0,r)

Find the slope of the line containing the points of tangency

`m=(0-r)/(r-0)=-1`

Remember that the equation of the line into slope intercept form is equal to

`y=mx+b`

where

m is the slope

b is the y-coordinate of the y-intercept

In this problem we have

`m=-1`

`b=r`

substitute

`y=-x+r`