# Equation of a Circle Problems

### Solutions

1Calculate the center coordinates and radius of the following circles, if applicable:

1

2

3

2Calculate the equation of the circle that has its center at (2, −3) and has the x-axis as a tangent.

3Calculate the equation of the circle that has its center at (−1, 4) and has the y-axis as a tangent.

4Calculate the equation of the circle which is centered at the point of intersection of the lines x + 3y + 3 = 0 and x + y + 1 = 0 and its radius is equal to 5.

5Find the equation of the circle which is concentric to the circle with equation , and passes through the point (−3, 4).

6A triangle with vertices A = (0, 0), B = (3, 1) and C = (5, 7) is inscribed in a circle. Calculate the equation of this circle.

7The ends of the diameter of a circle are the points A = (−5, 3) and B = (3, 1). What is the equation of this circle?

8Find the equation of the concentric circle to the circle which has a tangent of 3x − 4y + 7 = 0.

9Determine the points of intersection for the circle x^{2} + y^{2} - 4x + 2y − 20 = 0 with the following lines:

1 x + 7y − 20 = 0

2 3x + 4y − 27 = 0

3 x + y − 10 = 0

10Determine the equation of the circle which has its center at C = (3, 1) and a tangent of 3x − 4y + 5 = 0.

11Find the equation of the circle that passes through the points A = (2, 1) and B = (−2, 3) and has its center on the line: x + y + 4 = 0.

12Calculate the equation of the circle that passes through the point (0, −3), whose radius is and whose center is on the angle bisector of the first and third quadrants.

## 1

Calculate the center coordinates and radius of the following circles, if applicable:

1

2

It is not a circle.

3

Divide by 4.

## 2

Calculate the equation of the circle that has its center at (2, −3) and has the x-axis as a tangent.

## 3

Calculate the equation of the circle that has its center at (−1, 4) and has the y-axis as a tangent.

## 4

Calculate the equation of the circle which is centered at the point of intersection of the lines x + 3y + 3 = 0 and x + y + 1 = 0 and its radius is equal to 5.

## 5

Find the equation of the circle which is concentric to the circle with equation , and passes through the point (−3, 4).

## 6

A triangle with vertices A = (0, 0), B = (3, 1) and C = (5, 7) is inscribed in a circle. Calculate the equation of this circle.

## 7

The ends of the diameter of a circle are the points A = (−5, 3) and B = (3, 1). What is the equation of this circle?

## 8

Find the equation of the concentric circle to the circle which has a tangent of 3x − 4y + 7 = 0.

## 9

Determine the points of intersection for the circle x^{2} + y^{2} - 4x + 2y − 20 = 0 with the following lines:

1 **x + 7y − 20 = 0**

2 **3x + 4y − 27 = 0**

3 **x + y - 10 = 0**

## 10

Determine the equation of the circle which has its center at C = (3, 1) and a tangent of 3x − 4y + 5 = 0.

## 11

Find the equation of the circle that passes through the points A = (2, 1) and B = (−2, 3) and has its center on the line: x + y + 4 = 0.

## 12

Calculate the equation of the circle that passes through the point (0, −3), whose radius is and whose center is on the angle bisector of the first and third quadrants.