Question

question 4 of 10
which of the following circles have their centers on the x - axis?
check all that apply.
a. $(x - 0)^2+(y - 5)^2 = 49$
b. $(x + 1)^2+(y - 7)^2 = 16$
c. $(x - 0)^2+(y - 0)^2 = 25$
d. $(x - 4)^2+(y - 0)^2 = 22$

Explanation:

Step1: Recall the standard form of a circle equation

The standard form of a circle equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center of the circle.

Step2: Analyze each option

• Option A: For the equation \((x - 0)^2+(y - 5)^2 = 49\), the center is \((0,5)\). Since \(k = 5

eq0\), the center is not on the \(x\) - axis.

• Option B: For the equation \((x + 1)^2+(y - 7)^2 = 16\) (which can be written as \((x-(-1))^2+(y - 7)^2 = 16\)), the center is \((-1,7)\). Since \(k = 7

eq0\), the center is not on the \(x\) - axis.

• Option C: For the equation \((x - 0)^2+(y - 0)^2 = 25\), the center is \((0,0)\). Since \(k = 0\), the center is on the \(x\) - axis.
• Option D: For the equation \((x - 4)^2+(y - 0)^2 = 22\), the center is \((4,0)\). Since \(k = 0\), the center is on the \(x\) - axis.

Answer:

C. \((x - 0)^2+(y - 0)^2 = 25\), D. \((x - 4)^2+(y - 0)^2 = 22\)