College Algebra Problems With Answers sample 7 : Equation of Circle

A set of college algebra problems on the equation of circles are presented. The solutions are at the bottom of the page. Helpful
tutorials on circles is included in this site.

Find the equation of a circle whose center is at the point (-2 , 3) and its diameter has a length of 10.

Find the center and the radius of the circle whose equation is given by x^{ 2} + 4x + y^{ 2} - 8y = 5.

Find an equation of the circle that is is tangent to both the x and y axes, with a radius of 4 and whose center is located in the second quadrant.

Find an equation of the circle whose center is at the point (-4 , 6) and passes through the point (1 , 2).

Find an equation of the circle whose center is at the point (-3 , 6) and is tangent to the y axis.

Find an equation of the circle whose center is at the point (2 , -5) and is tangent to the x axis.

Find an equation of the circle whose diameter has endpoints at (-5 , 2) and (3 , 6).

Find the x and y intercepts of the graph of the circle given by the equation
x^{ 2} + 3x + y^{ 2} - 4y = 18

Is point A(-3 , 8) inside, outside or on the circle whose equation is given by
x^{ 2} + 4x + y^{ 2} - 8y = 5

Find the points of intersection of the circle with equation
(x - 2)^{ 2} + (y - 6)^{ 2} = 40
and the line with equation y = 3x

Three points are defined as follows: A(-2 , 1), B(6 , 1) and C(-2 , 7).

a) Find the midpoint M of segment BC.

b) Find the lengths of the line segments MA, MB and MC.

c) Find the equation of the circle that passes through the three points A, B and C.