#1
What is the standard form of the equation of a circle?
x^2 + y^2 = r^2
ExplanationCircle equation with center at the origin.
#2
Which of the following is the center-radius form of the equation of a circle?
(x - h)^2 + (y - k)^2 = r^2
ExplanationCircle equation centered at (h, k) with radius r.
#3
Which of the following is the equation of a circle with center (0,0) and radius 3?
x^2 + y^2 = 9
ExplanationCircle equation centered at the origin with radius 3.
#4
Which of the following is the equation of a circle with center (2,-5) and radius 7?
(x - 2)^2 + (y + 5)^2 = 7^2
ExplanationCircle equation centered at (2,-5) with radius 7.
#5
What is the equation of the circle with center (1,4) and radius 3?
(x - 1)^2 + (y - 4)^2 = 3^2
ExplanationCircle equation centered at (1,4) with radius 3.
#6
What is the standard form of the equation of a circle with center (-2,5) and radius 4?
(x + 2)^2 + (y - 5)^2 = 16
ExplanationCircle equation centered at (-2,5) with radius 4.
#7
What is the equation of the circle with center (3,-1) and radius 2?
(x - 3)^2 + (y + 1)^2 = 4
ExplanationCircle equation centered at (3,-1) with radius 2.
#8
What does the radius represent in the equation of a circle?
The distance from the center to any point on the circle
ExplanationDistance from the center to any point on the circle.
#9
What is the equation of the circle with center (2, -3) and radius 5?
(x - 2)^2 + (y + 3)^2 = 5^2
ExplanationCircle equation with center at (2, -3) and radius 5.
#10
What is the equation of the circle passing through the points (1,2), (3,4), and (5,6)?
(x - 1)^2 + (y - 2)^2 = (x - 3)^2 + (y - 4)^2 = (x - 5)^2 + (y - 6)^2
ExplanationEquation of circle passing through given points.
#11
Which of the following is the center-radius form of the equation of a circle with center (4,-2) and radius 6?
(x - 4)^2 + (y + 2)^2 = 36
ExplanationCircle equation centered at (4, -2) with radius 6.
#12
In the equation of a circle, what does the value 'h' represent?
The x-coordinate of the center
ExplanationX-coordinate of the circle's center.
#13
What is the equation of the circle with center (0,0) and passing through the point (5,12)?
x^2 + y^2 = 169
ExplanationCircle equation centered at the origin passing through (5,12).
#14
In the equation of a circle, what does the value 'k' represent?
The y-coordinate of the center
ExplanationY-coordinate of the circle's center.
#15
What is the general equation of a circle?
x^2 + y^2 + Dx + Ey + F = 0
ExplanationGeneral form of a circle equation with coefficients D, E, and F.
#16
What is the equation of a circle with center (-3,4) and passing through the point (2,1)?
(x + 3)^2 + (y - 4)^2 = 50
ExplanationCircle equation centered at (-3,4) passing through (2,1).
#17
What is the equation of a circle with center (-1,3) and radius 5?
(x + 1)^2 + (y - 3)^2 = 25
ExplanationCircle equation centered at (-1,3) with radius 5.
#18
What is the standard form of the equation of a circle in three-dimensional space?
x^2 + y^2 + z^2 = r^2
ExplanationEquation of a circle in 3D space.
#19
In the equation of a circle, what does the value 'r' represent?
The distance from the center to any point on the circle
ExplanationRadius of the circle.
#20
What is the equation of a circle with center (-2, 5) and passing through the point (1, -1)?
(x + 2)^2 + (y - 5)^2 = 40
ExplanationCircle equation centered at (-2, 5) passing through (1, -1).
#21
What is the equation of the circle with center (3, 7) and radius 8?
(x - 3)^2 + (y - 7)^2 = 64
ExplanationCircle equation centered at (3, 7) with radius 8.