Circles

Problem: 1

Write the standard form of the equation of the circle with radius 2 and center at the origin.

Problem: 3

Write the standard form of the equation of the circle with the given radius √ 5 and whose center is the origin.

Problem: 5

Write an equation and graph a circle with center (–1, 1) and radius 6.

Problem: 7

Write an equation and graph a circle with center (–3, –4) and radius 3.

Problem: 9

Find the equation of the circle with center (1.5, 0.3) and r = 11.5 units.

Problem: 11

Consider the circle (x + 5)² + (y – 7)² = 41.

Find its center and radius.

Problem: 13

Graph the equation and then write the radius of the circle.

x² + y² = 25

Problem: 15

Graph the equation and then write the radius of the circle.

7x² + 7y² = 196

Problem: 17

Graph the functions:

Identify the conic and write its equation.

Problem: 19

Graph the circle (x – 3)² + (y – 2)² = 4.

Problem: 21

Graph the circle (x – 5)² + y ² = 25.

Problem: 23

Say whether the point (0, 0) lies on the circle with equation x² + y² = 50².

Problem: 25

Write the standard form of the equation of the circle that passes through the point (0, –12) and whose center is the origin.

Problem: 27

Write the standard form of the equation of the circle that passes through the given point (–6, –8) and whose center is the origin.

Problem: 29

Write the standard form of the equation of the circle that passes through the given point (5, –2) and whose center is the origin.

Problem: 31

Find an equation of circle that has a diameter with endpoints (4, 3) and (0, 5).

Problem: 33

A circle has a radius of 4 units and the center of the circle is in the third quadrant. The circle is tangent to the y–axis. The center lies on the graph of y = 3x. Find the equation of the circle.

Problem: 35

Write an equation of the line that is tangent to the circle x² + y² = 26 at the point (1, 5)

Problem: 37

Write an equation of the line that is tangent to the circle x² + y² = 85 at the point (–6, –7).

Problem: 39

Find the points of intersection of the following graphs:

x² + y² = 1

Problem: 41

Find the points of intersection of the following graphs:

x² +y² = 4

x – y = –1

Problem: 43

Suppose a radar can detect incoming vehicles into the city as far as up to180 miles away. Which point is not within the range of the radar?

A. (150, 50)

B. (135, 150)

C. (60, 160)

D. (40, 168)

Problem: 45

Obtain the y–coordinates of all points where x = –5 on a circle with equation x² + y² = 169.

Problem: 1

Write the standard form of the equation of the circle with radius 2 and center at the origin.

Problem: 3

Write the standard form of the equation of the circle with the given radius √ 5 and whose center is the origin.

Problem: 5

Write an equation and graph a circle with center (–1, 1) and radius 6.

Problem: 7

Write an equation and graph a circle with center (–3, –4) and radius 3.

Problem: 9

Find the equation of the circle with center (1.5, 0.3) and r = 11.5 units.

Problem: 11

Consider the circle (x + 5)² + (y – 7)² = 41.

Find its center and radius.

Problem: 13

Graph the equation and then write the radius of the circle.

x² + y² = 25

Problem: 15

Graph the equation and then write the radius of the circle.

7x² + 7y² = 196

Problem: 17

Graph the functions:

Identify the conic and write its equation.

Problem: 19

Graph the circle (x – 3)² + (y – 2)² = 4.

Problem: 21

Graph the circle (x – 5)² + y ² = 25.

Problem: 23

Say whether the point (0, 0) lies on the circle with equation x² + y² = 50².

Problem: 25

Write the standard form of the equation of the circle that passes through the point (0, –12) and whose center is the origin.

Problem: 27

Write the standard form of the equation of the circle that passes through the given point (–6, –8) and whose center is the origin.

Problem: 29

Write the standard form of the equation of the circle that passes through the given point (5, –2) and whose center is the origin.

Problem: 31

Find an equation of circle that has a diameter with endpoints (4, 3) and (0, 5).

Problem: 33

A circle has a radius of 4 units and the center of the circle is in the third quadrant. The circle is tangent to the y–axis. The center lies on the graph of y = 3x. Find the equation of the circle.

Problem: 35

Write an equation of the line that is tangent to the circle x² + y² = 26 at the point (1, 5)

Problem: 37

Write an equation of the line that is tangent to the circle x² + y² = 85 at the point (–6, –7).

Problem: 39

Find the points of intersection of the following graphs:

x² + y² = 1

x + y = 1

Problem: 41

Find the points of intersection of the following graphs:

x² + y² = 4

x – y = –1

Problem: 43

Suppose a radar can detect incoming vehicles into the city as far as up to180 miles away. Which point is not within the range of the radar?

A. (150, 50)

B. (135, 150)

C. (60, 160)

D. (40, 168)

Problem: 45

Obtain the y–coordinates of all points where x = –5 on a circle with equation x² + y² = 169.

Hotmath Practice Problems