How do you find the equation of a circle that is tangent to both the x and y-axes and is tangent to the line 3x + 4y = 60 at the point (8,9)?

Answer 1

(9 - x)/(8 - x) = 4/3

x = 5

The center is at (5, 5) and the radius is 5.

Note that the distance from (5, 5) to (8,9) is 5, as is the distance to (5, 0) and (-5, 0)

Answer 2

Draw and label a diagram

A radius is perpendicular to the point of tangency.

Determine the equation of the perpendicular line passing though I8, 9)

The perpendicular line must pass through the center.

The center is equidistant from both axes (circle is tangent)

Center is (x, x) or (y, y). Substitute either into equation of perpendicular.

This gives coordinates of center.

Determine distance from center to (8, 9). This give radius.

Substitute values into appropriate formula.