The equation of a circle whose center is at (1, 2) and radius is 5 is

(x − 1)² + (y − 2)² = 25

Step-by-step explanation:

Equation of a circle is (x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius.

(x-1)^2+(y-2)^2=25
hope this helps!

[tex]\bf \textit{equation of a circle}\\\\ 
(x- h)^2+(y- k)^2= r^2
\qquad 
center~~(\stackrel{1}{ h},\stackrel{2}{ k})\qquad \qquad 
radius=\stackrel{5}{ r}
\\\\\\\
(x-1)^2+(y-2)^2=5^2\implies (x-1)^2+(y-2)^2=25[/tex]

The answer is [tex](x-1)^2+(y-2)^2=25[/tex]

Step-by-step explanation:

In order to determine the equation of a circle, we have to know the formula about it.

The "standard form equation of a circle" is:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where:

(h,k)= coordinates of the center of the circle. "h" is the "x" coordinate and "k" is the "y" coordinate.

r=radius of the circle.

So, we just need the center and radius to get the equation of a circle.

In this case:

[tex](h,k)=(1,2)\\r=5\\\\(x-1)^2+(y-2)^2=(5)^2\\(x-1)^2+(y-2)^2=25[/tex]

I have attached an image that shows a graph of a circle.

The equation is (x - 1)² + (y - 2)² = 25

Step-by-step explanation:

Knowing that the equation of a circle is (view image, extracted https://www.google.com/search?q=ecuacion+circulo&rlz=1C1CHZL_esAR816AR816&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiMkvnGlcbjAhUbIrkGHX37AaMQ_AUIESgB&biw=1366&bih=608#imgrc=7ejmEpSWiG0WAM: )

Then, a and b represent the x and y value of the circle's center, and r^2, is the square of the radius.

Then, if we have that the center is (1,2) and the radius is 5:

[tex](x-1)^{2}(y-2)^{2} =5^{2} =25[/tex]