Duplicate Question
The question on this page has been marked as a duplicate question.
Original 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...Question
A circle is drawn on a coordinate plane with the center point at (−8,−2)
and a radius of 2. Derive the equation of the circle in standard form, using the given information and the Pythagorean Theorem.(1 point)
Responses
(x−2)2+(y−8)2=2
left parenthesis x minus 2 right parenthesis squared plus left parenthesis y minus 8 right parenthesis squared equals 2
(x+2)2+(y+8)2=2
left parenthesis x plus 2 right parenthesis squared plus left parenthesis y plus 8 right parenthesis squared equals 2
(x+8)2+(y+2)2=4
left parenthesis x plus 8 right parenthesis squared plus left parenthesis y plus 2 right parenthesis squared equals 4
(x−8)2+(y−2)2=4
and a radius of 2. Derive the equation of the circle in standard form, using the given information and the Pythagorean Theorem.(1 point)
Responses
(x−2)2+(y−8)2=2
left parenthesis x minus 2 right parenthesis squared plus left parenthesis y minus 8 right parenthesis squared equals 2
(x+2)2+(y+8)2=2
left parenthesis x plus 2 right parenthesis squared plus left parenthesis y plus 8 right parenthesis squared equals 2
(x+8)2+(y+2)2=4
left parenthesis x plus 8 right parenthesis squared plus left parenthesis y plus 2 right parenthesis squared equals 4
(x−8)2+(y−2)2=4
Answers
Answered by
GPT-4o mini
To derive the equation of the circle in standard form, we use the following formula for the equation of a circle:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
Given:
- Center \((h, k) = (-8, -2)\)
- Radius \(r = 2\)
1. Substitute the values of \(h\), \(k\), and \(r\) into the formula:
\[
(x - (-8))^2 + (y - (-2))^2 = 2^2
\]
2. Simplify this:
\[
(x + 8)^2 + (y + 2)^2 = 4
\]
Thus, the equation of the circle in standard form is:
\[
\boxed{(x + 8)^2 + (y + 2)^2 = 4}
\]
This corresponds to the response:
\((x+8)^2+(y+2)^2=4\).
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
Given:
- Center \((h, k) = (-8, -2)\)
- Radius \(r = 2\)
1. Substitute the values of \(h\), \(k\), and \(r\) into the formula:
\[
(x - (-8))^2 + (y - (-2))^2 = 2^2
\]
2. Simplify this:
\[
(x + 8)^2 + (y + 2)^2 = 4
\]
Thus, the equation of the circle in standard form is:
\[
\boxed{(x + 8)^2 + (y + 2)^2 = 4}
\]
This corresponds to the response:
\((x+8)^2+(y+2)^2=4\).
There are no human answers yet. A form for humans to post answers is coming very soon!