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

Answer:

$y=-x+r$

Step-by-step 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

$m=\frac{0-r}{r-0}=-1$

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

$y=-x+r$