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.

 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: x2 + y2 + 6x - 10 y = 9 Questions 8: Find the center and radius of the circle whose equation is given by: x2 + y2 + 4y = 0 Questions 9: Find the center and radius of the circle whose equation is given by: -x2 - y2 + 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 x2 + y2 = 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 + y2 = 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 x2 + y2 = K? Questions 17: Is the point (3 , 5) inside, outside or on the circle with equation x2 + y2 = 9? Questions 18: For what value of K is the point (1 , K) inside the circle with equation x2 + y2 = 4? Questions 19: For what value of K is the point (K , -2) outside the circle with equation x2 + y2 = 9? Questions 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 More math questions and problems with detailed solutions in this site.