Question

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

Answer 1

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

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`.