Question

page 8 of 8 Equation of a Circle Quick Check 1 of 51 of 5 Items Question A circle is drawn on a coordinate plane with the center point at (−1,3) and a radius of 5. Derive the equation of the circle in standard form, using the given information and the Pythagorean Theorem.(1 point) Responses (x+3)2+(y−1)2=25 left parenthesis x plus 3 right parenthesis squared plus left parenthesis y minus 1 right parenthesis squared equals 25 (x+1)2+(y−3)2=25 left parenthesis x plus 1 right parenthesis squared plus left parenthesis y minus 3 right parenthesis squared equals 25 (x−3)2+(y−1)2=25 left parenthesis x minus 3 right parenthesis squared plus left parenthesis y minus 1 right parenthesis squared equals 25 (x−1)2+(y−3)2=25 left parenthesis x minus 1 right parenthesis squared plus left parenthesis y minus 3 right parenthesis squared equals 25 Skip to navigation

Answer 1

To derive 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 your case, the center of the circle is given as \((-1, 3)\) (thus \(h = -1\) and \(k = 3\)) and the radius is \(5\).

First, you will need to calculate \(r^2\): \[ r^2 = 5^2 = 25 \]

Now, substitute the values of \(h\), \(k\), and \(r^2\) into the standard form equation:

\[ (x - (-1))^2 + (y - 3)^2 = 25 \]

This simplifies to:

\[ (x + 1)^2 + (y - 3)^2 = 25 \]

So, the correct equation of the circle in standard form is:

\[ (x + 1)^2 + (y - 3)^2 = 25 \]

Among the options you provided, the correct response is:

\[ (x + 1)^2 + (y - 3)^2 = 25 \]