Answer:
Option B. (x+3) ^2+(y+4)^2=25
Step-by-step explanation:
we know that
The equation of the circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center and r is the radius
step 1
Find the radius of the circle
Remember that the distance of the center and any point on the circle is equal to the radius of the circle
so
Find the distance between the points (-3,-4) and (0,0)
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute
[tex]r=\sqrt{(0+4)^{2}+(0+3)^{2}}[/tex]
[tex]r=\sqrt{(4)^{2}+(3)^{2}}[/tex]
[tex]r=\sqrt{25}[/tex]
[tex]r=5\ units[/tex]
step 2
Find the equation of the circle
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
the center is the point (-3,-4) and the radius is r=5 units
substitute
[tex](x+3)^{2}+(y+4)^{2}=5^{2}[/tex]
[tex](x+3)^{2}+(y+4)^{2}=25[/tex]
