Answer:
(x - 4)² + (y + 7)² = 81
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (4, - 7) and r = 9, thus
(x - 4)² + (y - (- 7))² = 9², that is
(x - 4)² + (y + 7)² = 81 ← equation of circle
This question is based on the equation of circle. Therefore, the equation of circle is (x - 4)² + (y + 7)² = 81 describes a circle with center (4, -7) and radius 9.
Given:
A circle with center (4, -7) and radius 9.
We need to determined the equation describes a circle with center (4, -7) and radius 9.
According to the question,
As we know that, the equation of a circle in standard form is
⇒ (x - h)² + (y - k)² = r²
Where (h, k) are the coordinates of the center and r is the radius.
Here, it is given that, (h, k) = (4, - 7) and r = 9.
Therefore, by putting the given values.
We get,
⇒ (x - 4)² + (y - (- 7))² = 9², that is
⇒ (x - 4)² + (y + 7)² = 81 ← equation of circle
Therefore, the equation of circle is (x - 4)² + (y + 7)² = 81 describes a circle with center (4, -7) and radius 9.
For more details, prefer this link:
https://brainly.com/question/8714903
