How do you find the general form of the equation of a circle given the center at the point (-3, 1) and tangent to the y-axis?

1 Answer
Oct 17, 2016

Answer:

Please see the explanation for the process. The equation of the circle is:

#(x - -3)^2 + (y - 1)^2 = 3^2#

Explanation:

The general equation for a circle is:

#(x - h)^2 + (y - k)^2 = r^2#

where #(h, k)# is the center point and #r# is the radius.

The center is #(-3, 1)#; this gives us the equation:

#(x - -3)^2 + (y - 1)^2 = r^2#

We are told that the y axis is tangent, therefore, the x coordinate is 0 and the y coordinate is the same as the center, 1. To find the value of r, temporarily substitute the point #(0,1)# for x and y in the equation:

#(0 - -3)^2 + (1 - 1)^2 = r^2#

#r = 3#

The equation of the circle is:

#(x - -3)^2 + (y - 1)^2 = 3^2#