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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) x² + 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