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 1Find the distance between the points A(3 , 4) and B(5 , 8)
Question 2Find x so that the distance between the points (x , 4) and (5 , 3) is equal to 5.
Question 3Write the equation of the circle with center at (0 , 0) and a radius of 6.
Question 4Find the center and radius of the circle whose equation is given by: (x  2)^{2} + (y + 5)^{2} = 13
Question 5Find the center and radius of the circle whose equation is given by: (5  x)^{2} + (y  1)^{2} = 4
Question 6Find the center and radius of the circle whose equation is given by: (4  x)^{2} + (y + 11)^{2} = 9
Question 7Find the center and radius of the circle whose equation is given by: x^{2} + y^{2} + 6x  10 y = 9
Question 8Find the center and radius of the circle whose equation is given by: x^{2} + y^{2} + 4y = 0
Question 9Find the center and radius of the circle whose equation is given by: x^{2}  y^{2} + 8x = 0
Question 10Find the equation of a circle that has a diameter with end points (6 , 1) and (2 , 5).
Question 11Find 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.
Question 12Find the equations of the circle with center at (3 , 5) and passes through the point (5 , 1).
Question 13Find the equations of the circle that passes through the points (0 , 6), (0 , 0) and (8 , 0).
Question 14Find the point of intersection of the circle with equation (x  2)^{2} + y^{2} = 8 and the line with equation y = x  2
Question 15For 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 16For what value of K will the line with equation x = 6 be tangent to the circle with equation x^{2} + y^{2} = K?
Question 17Is the point (3 , 5) inside, outside or on the circle with equation x^{2} + y^{2} = 9?
Question 18For what value of K is the point (1 , K) inside the circle with equation x^{2} + y^{2} = 4?
Question 19For what value of K is the point (K , 2) outside the circle with equation x^{2} + y^{2} = 9?
Question 20For what value of K is the point (K , 2K) on the circle with equation x^{2} + y^{2} = 5?
ANSWERS TO ABOVE QUESTIONS1) 2 √(5)2) x = 7 , x = 3 3) x^{2} + y^{2} = 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 Linkscenter and radius of the circlemath questions and problems with detailed solutions .
