Question

Circles In these exercise we find the equations of circles.

Find an equation of circle that has center $\left(2,-5\right)$and radius $\sqrt{2}$.

Short answer

The equation of the circle is ${\left(x-2\right)}^2+{\left(y+5\right)}^2=2$.

Step-by-step solution

Step 1. Write the given information.

The center of the circle is $\left(2,-5\right)$.

The radius of the circle is $\sqrt{2}$.

Step 2. Write the equation of circle.

The standard equation of circle is given by,

${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2\mathrm{...}\left(1\right)$

Here,$\left(h,k\right)$ is the center the of the circle and r is the radius of the circle.

Step 3. Find the equation of circle.

Substitute 2 for h,$-5$ for k and$\sqrt{2}$ for r in equation (1).

$\begin{array}{c}{\left(x-2\right)}^2+{\left(y-\left(-5\right)\right)}^2={\left(\sqrt{2}\right)}^2\\ {\left(x-2\right)}^2+{\left(y+5\right)}^2=2\end{array}$

Thus, the equation of the circle is ${\left(x-2\right)}^2+{\left(y+5\right)}^2=2$.