Answer:
1. option D is correct; [tex](x+2)^2+(y+7)^2=36[/tex]
2. option C is correct; center: (-4, 5) and radius = 11 unit
Step-by-step explanation:
The general equation of the circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex] .....[1]
where,
(h, k) is the center of the circle and r is the radius of the circle.
1.
As per the statement:
The center of a circle is at (−2, −7) and its radius is 6.
⇒(h, k) = (-2, -7) and r = 6 units
Substitute these in [1] we have;
[tex](x-(-2))^2+(y-(-7))^2=6^2[/tex]
⇒[tex](x+2)^2+(y+7)^2=36[/tex]
Therefore, the equation of circle is, [tex](x+2)^2+(y+7)^2=36[/tex]
2.
As per the statement:
The equation of a circle is:
[tex](x+4)^2+(y-5)^2 = 121[/tex]
We can write this as:
[tex](x-(-4))^2+(y-5)^2 = 11^2[/tex]
On comparing with equation [1] we have;
(h, k) = (-4, 5) and r = 11 units
Therefore, the center and radius of the circle is,
center: (-4, 5) and radius = 11 unit
