# Math Questions With Answers (5): Circles

A set of math questions on circles and distance bewteen two points are presented. Answers to these questions are also provided and are located at the lower part of the page.

## Question 1

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

## Question 2

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

## Question 3

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

## Question 4

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

## Question 5

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

## Question 6

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

## Question 7

Find the center and radius of the circle whose equation is given by: x2 + y2 + 6x - 10 y = 9

## Question 8

Find the center and radius of the circle whose equation is given by: x2 + y2 + 4y = 0

## Question 9

Find the center and radius of the circle whose equation is given by: -x2 - y2 + 8x = 0

## Question 10

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

## Question 11

Find the point(s) of intersection of the circle with equation x2 + y2 = 4 and the circle with equations (x - 2)2 + (y - 2)2 = 4.

## Question 12

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

## Question 13

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

## Question 14

Find the point of intersection of the circle with equation (x - 2)2 + y2 = 8 and the line with equation y = x - 2

## Question 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?

## Question 16

For what value of K will the line with equation x = 6 be tangent to the circle with equation x2 + y2 = K?

## Question 17

Is the point (3 , 5) inside, outside or on the circle with equation x2 + y2 = 9?

## Question 18

For what value of K is the point (1 , K) inside the circle with equation x2 + y2 = 4?

## Question 19

For what value of K is the point (K , -2) outside the circle with equation x2 + y2 = 9?

## Question 20

For what value of K is the point (K , 2K) on the circle with equation x2 + y2 = 5?

## ANSWERS TO ABOVE QUESTIONS

1) 2 √(5)
2) x = -7 , x = -3
3) x
2 + y2 = 36
4) center at (2 , -5) , radius = √(13)
5) center at (5 , 1) , radius = 2
6) center at (-4 , 11) , radius = 3
7) center at (-3 , 5) , radius = √(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 √(19)) / 20 = 1.7 (approximated to one decimal place)
and K = (21 - 3 √(19)) / 20 = 0.4 (approximated to one decimal place)
16) K = 36
17) Outside
18) -√(3) < K < √(3)
19) K may have any value in the interval ( - infinity , -√(5) ) U ( √(5) + infinity)
20) K = 1, K = -1

## More References and Links

center and radius of the circle
math questions and problems with detailed solutions .