Question: 2 of 40: Which of the following circle equations represents a circle whose center is at (0, 0)?Select one of the options below as your answer: A. x2 + y2 = 45 B. (x − 3)2 + (y − 5)2 = 0 C. (x + 3)2 + (y − 3)2 = 0 D. x2 + (y − 1)2 = 1
No it isn't.For example:
when (x-2)^2+(y-3)^2=16 equation,whose center is (2,3) and radius is 4.
there is an only a is true.Because whose center coordinate is (0,0).
The equation x2 + y2 − 2x + 2y − 1 = 0 is the general form of the equation of a circle. What is the standard form of the equation?
To determine which of the given circle equations represents a circle with a center at (0, 0), we can look at the general equation of a circle.
The general equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius.
Let's analyze each option:
A. x^2 + y^2 = 45:
This equation does not have any terms with (x - h) or (y - k), indicating that its center is at the origin (0, 0). Therefore, option A represents a circle with a center at (0, 0).
B. (x - 3)^2 + (y - 5)^2 = 0:
In this equation, the terms (x - 3) and (y - 5) indicate that the center of the circle is at (3, 5), not at (0, 0). Therefore, option B does not represent a circle with a center at (0, 0).
C. (x + 3)^2 + (y - 3)^2 = 0:
Similar to option B, this equation has the terms (x + 3) and (y - 3), indicating that the center of the circle is at (-3, 3), not at (0, 0). Therefore, option C does not represent a circle with a center at (0, 0).
D. x^2 + (y - 1)^2 = 1:
Again, this equation has the term (y - 1), meaning that the center of the circle is at (0, 1), not at (0, 0). Therefore, option D does not represent a circle with a center at (0, 0).
Therefore, the correct answer is option A: x^2 + y^2 = 45.