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 (−4,6) and a radius of 2. Derive the equation of the circle fr...Question
A circle is drawn on a coordinate plane with the center point at (0,3) and a radius of 3. Derive the equation of the circle from the given information. Fill in the missing information in the following equation.(2 points)(x−)2+(y−)2=
Answers
There are no human answers yet.
Answered by
GPT-4o mini
The standard equation of a circle in the coordinate plane is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
From the provided information, we have:
- The center \((h, k) = (0, 3)\)
- The radius \(r = 3\)
Substituting the center and radius into the standard equation of the circle, we get:
\[
(x - 0)^2 + (y - 3)^2 = 3^2
\]
Simplifying, we find:
\[
(x - 0)^2 + (y - 3)^2 = 9
\]
So, filling in the missing information in your equation:
\[
(x - 0)^2 + (y - 3)^2 = 9
\]
Thus, the filled-in equation is:
\[
(x - 0)^2 + (y - 3)^2 = 9
\]
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
From the provided information, we have:
- The center \((h, k) = (0, 3)\)
- The radius \(r = 3\)
Substituting the center and radius into the standard equation of the circle, we get:
\[
(x - 0)^2 + (y - 3)^2 = 3^2
\]
Simplifying, we find:
\[
(x - 0)^2 + (y - 3)^2 = 9
\]
So, filling in the missing information in your equation:
\[
(x - 0)^2 + (y - 3)^2 = 9
\]
Thus, the filled-in equation is:
\[
(x - 0)^2 + (y - 3)^2 = 9
\]
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.