FIND CENTER AND RADIUS OF A CIRCLE FROM AN EQUATION WORKSHEET

Write down the center and radius of each circle below

Problem 1 :

x² + y² = 25

Solution

Problem 2 :

x² + y² = 12

Solution

Problem 3 :

(x – 3)² + (y – 2)² = 36

Solution

Problem 4 :

(x + 1)² + (y – 4)² = 10

Solution

Problem 5 :

x² + y² – 10x – 6y - 2 = 0

Solution

Problem 6 :

x² + y² + 6x + 4y + 4 = 0

Solution

Problem 7 :

The point (a, 5) lies on the circle with equation x² + y² = 74. Find two values for a.          Solution

Problem 8 :

The point (3, c) lies on the circle x² + y² – 4x + 6y + 12 = 0. Find c.

Solution

Problem 9 :

Two circles have equations

(x + 1)² + (y + 3)² = 20 and x² + y² – 10x – 18y + 26 = 0

(a) Write down the center and radius of each circle.

(b) Show that the circles touch at a single point.

(c) Find P, the point of contact of the circles.

Solution

Problem 1 :

x² + 10x + y² – 6y = -18

The graph of the equation shown above is a circle. What is the radius of the circle?

A) 3    B) 4     C) 5    D) 9

Solution

Problem 2 :

x² + 18x + y² – 8y = -48

The graph of the equation shown above is a circle. What is the radius of the circle?

A) 4    B) 5    C) 6     D) 7

Solution

Problem 3 :

x² - 4x + y² + 6y = 113

The graph of the equation shown above is a circle. What is the coordinate point of the center of the circle?

A) (13, 10)    B) (4, 13)     C) (-4, 6)     D) (2, -3)

Solution

Problem 4 :

What is the circumference of the circle in the xy-plane with equation ?

(x + 7)² + (y - 5)² = 100 ?

a) 10π      b)  20π     c)  100π     d)  200π

Solution

Problem 5 :

Circle A has an area of 32π and circle B has an area of 384π. The radius of the circle B is how many times longer than the radius of circle A ?

a) 2√3     b)  3√2     c)  6    d) 12

Solution

Problem 6 :

A circle in the xy-plane has the equation 

x² + y² = 9

The line y = 0 intersects this circle at two points. Which of the following is one of the points of intersection ?

a)  (-3, 0)         b) (0, -3)        c)  (0, 0)       d) (0, 3)

Solution

Problem 7 :

Circle A in the xy-plane has the equation 

(x - 1)² + (y + 2)² = 64

Circle B is obtained by shifting circle A up 7 units, Which of the following equations represents circle B?

a) (x - 1)² + (y - 9)² = 64                b)  (x - 1)² + (y + 9)² = 64 

c) (x - 1)² + (y - 5)² = 64                d)  (x - 1)² + (y + 5)² = 64 

Solution

Find the equation of circle with the center and passes through the given point.

Problem 1 :

Center : (11, 0)

Point on Circle : (3, 0)

Solution

Problem 2 :

Center : (15, 13)

Point on Circle : (19, 13)

Solution

Problem 3 :

Center : (-5, 9)

Point on Circle : (-7, 11)

Solution

Problem 4 :

Center : (-11, 11)

Point on Circle : (-15, 17)

Solution

Problem 5 :

Find the equation of a circle where the center is at (2, -4), and the point (6, 1) rests on the circle.

Solution

Problem 6 :

Find the equation of a circle where the center is at (-2, 3), and the point (1, 4) rests on the circle.

Solution