Answer:
The answer is 5 cm.
Step-by-step explanation:
Since the center is (0,4) and one of the point lies on (-2,-1),
4 - (-1) = 5 cm
The radius of a circle with center at [tex]C (0, 4)[/tex] and point [tex]P(-2, -1)[/tex] will be [tex]\sqrt{29}[/tex].
Equation of a circle is written in the form of [tex](x-h)^2+(y-k)^2=r^2[/tex] where [tex](h,k)[/tex] represents the center and [tex]r[/tex] is the radius.
We have,
Center at [tex]C (0, 4)[/tex]
i.e. [tex]h=0,\ k=4[/tex]
And,
Point [tex]P(-2, -1)[/tex]
i.e. [tex]x=-2,\ y=-1[/tex]
Now,
To determine Radius of the circle;
[tex]r^2=(x-h)^2+(y-k)^2[/tex]
[tex]r^2=(-2-0)^2+(-1-4)^2[/tex]
[tex]r^2=(-2)^2+(-5)^2[/tex]
[tex]r=\sqrt{4+25}[/tex]
[tex]r=\sqrt{29}[/tex]
So, radius of the circle is [tex]\sqrt{29}[/tex] , which is find out using equation of a circle.
Hence, we can say that the radius of a circle with center at [tex]C (0, 4)[/tex] and point [tex]P(-2, -1)[/tex] will be [tex]\sqrt{29}[/tex].
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