91Ó°ÊÓ

The given center = (2, 5) and radius = 3.

We have to find the equation of the circle.

We know that the standard form of the equation of a circle with center (a, b) and radius r is${\left(x−a\right)}^2+{\left(y−b\right)}^2=r^2$ .

From the given equation, the center (a, b) = (2, 5) and radius = r = 3.

Plug them in the standard form of the circle.

So, the equation of the circle is${\left(x−2\right)}^2+{\left(y−5\right)}^2={\left(3\right)}^2$ .

Or,${\left(x−2\right)}^2+{\left(y−5\right)}^2=9$ .

The given center = (-2, 0) and radius = 5.

We have to find the equation of the circle.

We know that the standard form of the equation of a circle with center (a, b) and radius r is${\left(x−a\right)}^2+{\left(y−b\right)}^2=r^2$ .

From the given equation, the center (a, b) = (-2, 0) and radius = r = 5.

Plug them in the standard form of the circle.

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

Or,${\left(x+2\right)}^2+y^2=25$ .

The given center = (-2, 3) and radius = 10.

We have to find the equation of the circle.

We know that the standard form of the equation of a circle with center (a, b) and radius r is${\left(x−a\right)}^2+{\left(y−b\right)}^2=r^2$ .

From the given equation, the center (a, b) = (-2, 3) and radius = r = 10.

Plug them in the standard form of the circle.

So, the equation of the circle is${\left(x+2\right)}^2+{\left(y−3\right)}^2={\left(10\right)}^2$ .

Or,${\left(x+2\right)}^2+{\left(y−3\right)}^2=100$ .

The given center = (j, k) and radius = n.

We have to find the equation of the circle.

We know that the standard form of the equation of a circle with center (a, b) and radius r is ${\left(x−a\right)}^2+{\left(y−b\right)}^2=r^2$.

From the given equation, the center (a, b) = (j, k) and radius = r = n.

Plug them in the standard form of the circle.

So, the equation of the circle is ${\left(x−j\right)}^2+{\left(y−k\right)}^2={\left(n\right)}^2$.

Or, ${\left(x−j\right)}^2+{\left(y−k\right)}^2=n^2$.