Question

Write the equation of a Circle with the given information.Center: (-4,7) Point on the Circle: (8,-4)

Answer 1

Given:

Center of circle: (-4, 7)

Endpoint on the circle: (8, -4)

Let's write the equation of the circle with the given information.

Apply the equation of a circle:

`(x-h)^2+(y-k)^2=r^2`

Where:

Center of circle: (h, k) ==> (-4, 7)

Radius = r

Substitute the values of (h, k) in the equation:

`\begin{gathered} (x-(-4))^2+(y-7)^2=r^2 \\ \\ (x+4)^2+(y-7)^2=r^2 \end{gathered}`

To find the radius, let's find the distance between the points (-4, 7) and (8, -4).

Apply the distance formula:

`d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}`

Given:

(x1, y1) ==> (-4, 7)

(x2, y2) ==> (8, -4)

Thus, we have:

`\begin{gathered} d=\sqrt[]{(-4-7)^2+(8-(-4))^2} \\ \\ d=\sqrt[]{(-4-7)^2+(8+4)^2} \\ \\ d=\sqrt[]{(11)^2+(12)^2} \\ \\ d=\sqrt[]{121+144} \\ \\ d=\sqrt[]{265} \\ \\ d=16.3 \end{gathered}`

Therefore, the radius is 16.3

Therefore, we have the equation of the circle as:

`(x+4)^2+(y-7)^2=16.3^2`

ANSWER:

`(x+4)^2+(y-7)^2=16.3^2`