Chapter 10.3, Problem 6AYU

To determine

To find: The standard equation of the circle with center at $\left(2,-3\right)$ and radius 1.

Answer to Problem 6AYU

Solution:

$\left(x-2\right)²+\left(y+3\right)²=1$

Explanation of Solution

Given:

Center: $\left(2,-3\right)$, Radius: 1.

Formula Used:

The standard form of an equation of a circle with radius $r$ and center $\left(h,k\right)$ is

${\left(x-h\right)}^2+{\left(y-k\right)}^2=r²$

Calculation:

Center: $\left(2,-3\right)$, Radius: 1.

Substituting in the formula ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r²$, we get,

$\left(x-2\right)²+\left(y-\left(-3\right)\right)²=1$

$\left(x-2\right)²+\left(y+3\right)²=1$