Answer:
Step-by-step explanation:
Equation for a circle of radius r, centered at (h,k):
(x-h)² + (y-k)² = r²
x² + (y+3)² = 9 is the equation for a circle of radius 3, centered at (0,-3).
Option D - Coordinate plane with no numbers marking the units. A circle is drawn on the plane, with the center at the labeled point begin ordered pair 0 comma negative 3 end ordered pair. The perimeter of the circle goes through the labeled point begin ordered pair negative 3 comma negative 3 end ordered pair IS CORRECT.
We have a equation of circle -
[tex]x^{2} +(y+3)^{2} = 9[/tex]
We have to find out which statement correctly represents the graph of this equation.
The general equation of the circle with radius r and center at (h, k)
is - [tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
The equation given to us is -
[tex]x^{2} +(y+3)^{2} = 9[/tex]
On comparing it with the general equation of the circle, we get -
[tex]x-h=x\\h=0\\\\y-k=y+3\\k=-3\\\\r^{2} =9\\r=3[/tex]
Therefore, we have a circle whose center lies at (0, -3) with radius = 3 units.
At point P(3, 3) -
[tex](-3)^{2}+(-3+3)^{2} =9\\9=9[/tex]
Hence, Option D - coordinate plane with no numbers marking the units. A circle is drawn on the plane, with the center at the labeled point begin ordered pair 0 comma negative 3 end ordered pair. The perimeter of the circle goes through the labeled point begin ordered pair negative 3 comma negative 3 end ordered pair is correct.
To solve more questions on the general equations of circle, visit the link below -
https://brainly.com/question/11711668
#SPJ2
