__Questions 1:__

Find the distance between the points A(3 , 4) and B(5 , 8)

__Questions 2:__

Find x so that the distance between the points (x , 4) and (-5 , 3) is equal to 5.

__Questions 3:__

Write the equation of the circle with center at (0 , 0) and a radius of 6.

__Questions 4:__

Find the center and radius of the circle whose equation is given by: (x - 2)^{2} + (y + 5)^{2} = 13

__Questions 5:__

Find the center and radius of the circle whose equation is given by: (5 - x)^{2} + (y - 1)^{2} = 4

__Questions 6:__

Find the center and radius of the circle whose equation is given by: (-4 - x)^{2} + (-y + 11)^{2} = 9

__Questions 7:__

Find the center and radius of the circle whose equation is given by: x^{2} + y^{2} + 6x - 10 y = 9

__Questions 8:__

Find the center and radius of the circle whose equation is given by: x^{2} + y^{2} + 4y = 0

__Questions 9:__

Find the center and radius of the circle whose equation is given by: -x^{2} - y^{2} + 8x = 0

__Questions 10:__

Find the equation of a circle that has a diameter with end points (-6 , 1) and (2 , -5).

__Questions 11:__

Find the point(s) of intersection of the circle with equation x^{2} + y^{2} = 4 and the circle with equations (x - 2)^{2} + (y - 2)^{2} = 4.

__Questions 12:__

Find the equations of the circle with center at (-3 , 5) and passes through the point (5 , -1).

__Questions 13:__

Find the equations of the circle that passes through the points (0 , 6), (0 , 0) and (8 , 0).

__Questions 14:__

Find the point of intersection of the circle with equation (x - 2)^{2} + y^{2} = 8 and the line with equation y = x - 2

__Questions 15:__

For what value of K will the line with equation y = K x be tangent to the circle with equation (x - 7)^{2} + (y - 6)^{2} = 9?

__Questions 16:__

For what value of K will the line with equation x = 6 be tangent to the circle with equation x^{2} + y^{2} = K?

__Questions 17:__

Is the point (3 , 5) inside, outside or on the circle with equation x^{2} + y^{2} = 9?

__Questions 18:__

For what value of K is the point (1 , K) inside the circle with equation x^{2} + y^{2} = 4?

__Questions 19:__

For what value of K is the point (K , -2) outside the circle with equation x^{2} + y^{2} = 9?

__Questions 20:__

For what value of K is the point (K , 2K) on the circle with equation x^{2} + y^{2} = 5?

**ANSWERS TO ABOVE QUESTIONS**

1) 2 SQRT(5)

2) x = -7 , x = -3

3) x^{2} + y^{2} = 36

4) center at (2 , -5) , radius = SQRT(13)

5) center at (5 , 1) , radius = 2

6) center at (-4 , 11) , radius = 3

7) center at (-3 , 5) , radius = SQRT(43)

8) center at (0 , -2) , radius = 2

9) center at (4 , 0) , radius = 4

10) (x + 2)^{2} + (y + 2)^{2} = 25

11) (2 , 0) and (0 , 2)

12) (x + 3)^{2} + (y - 5)^{2} = 100

13) (x - 4)^{2} + (y - 3)^{2} = 25

14) (0 , -2) and (4 , 2)

15) K = (21 + 3 SQRT(19)) / 20 = 1.7 (approximated to one decimal place)

and K = (21 - 3 SQRT(19)) / 20 = 0.4 (approximated to one decimal place)

16) K = 36

17) Outside

18) -SQRT(3) < K < SQRT(3)

19) K may have any value in the interval ( - infinity , -SQRT(5) ) U ( SQRT(5) + infinity)

20) K = 1, K = -1

More math questions and problems with detailed solutions in this site.