Question

Write the standard equation for the circle whose center is at ​(6​,2​) and whose radius is 2.

Answer 1

Answer:

$(x - 6)^2 + (y - 2)^2 = 2^2$.

Step-by-step explanation:

In general, let $(a,\, b)$ denote the center of a given circle. Let $r$ denote the radius of that circle. The standard equation for that circle would be:

$(x - a)^2 + (y - b)^2 = r^2$.

The circle in this question is centered at $(6,\, 2)$.  

• $6$ is the $x$-coordinate of the center of this circle. $a = 6$.
• $2$ is the $y$-coordinate of the center of this circle. $b = 2$.

The radius of this circle is $2$. Therefore, $r = 2$.

Hence, the standard equation for this circle would be:

$(x - 6)^2 + (y - 2)^2 = 2^2$.