Question

Question

Given the center left parenthesis lower h comma lower k right parenthesis equals left parenthesis 5 comma 0 right parenthesis and radius lower r equals 3, write an equation for the circle in standard form.
(1 point)
Responses

left parenthesis x plus 5 right parenthesis squared plus y squared equals 9
Image with alt text: left parenthesis x plus 5 right parenthesis squared plus y squared equals 9

left parenthesis x minus 5 right parenthesis squared plus y squared equals 9
Image with alt text: left parenthesis x minus 5 right parenthesis squared plus y squared equals 9

left parenthesis x minus 5 right parenthesis squared plus y equals 3
Image with alt text: left parenthesis x minus 5 right parenthesis squared plus y equals 3

left parenthesis x minus 5 right parenthesis squared plus y squared equals 3
Image with alt text: left parenthesis x minus 5 right parenthesis squared plus y squared equals 3
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Answer 1

To write the equation of a circle in standard form, you can use the formula:

\[ (x - h)^2 + (y - k)^2 = r^2 \]

where \((h, k)\) is the center of the circle and \(r\) is the radius.

In this case, you are given:

• Center \((h, k) = (5, 0)\)
• Radius \(r = 3\)

Now, substituting these values into the formula, we have:

\[ (x - 5)^2 + (y - 0)^2 = 3^2 \]

This simplifies to:

\[ (x - 5)^2 + y^2 = 9 \]

Now, comparing this with your options, the correct equation for the circle in standard form is:

\[ \left( x - 5 \right)^2 + y^2 = 9 \]

Therefore, the correct response is:

left parenthesis x minus 5 right parenthesis squared plus y squared equals 9