To answer this question, we need to remember the equation for a circle with a center at point (h, k) is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]We have that the center of this circle is located at point (0, 4). Then, we have:
• h = 0
,• k = 4
And we also know that the point (-2, -1) lies on this circle. Then, we have:
• x = -2
,• y = -1
Therefore, we can substitute these values into the previous equation to find the radius of this circle as follows:
[tex](-2-0)^2+(-1-4)^2_{}=r^2\Rightarrow r^2=(-2)^2+(-5)^2\Rightarrow r^2=4+25[/tex]Now, we finally have that the length of the radius of this circle is (squared root of 29 units) (third option):
[tex]r^2=29\Rightarrow\sqrt[]{r^2}=\sqrt[]{29}\Rightarrow r=\sqrt[]{29}[/tex]We can represent graphically the equation of the circle as follows:
[tex](x-0)^2+(y-4)^2=(\sqrt[]{29})^2=(x-0)^2+(y-4)^2=29[/tex]
