Question

Write the equation of a Circle with the given information.End points of a diameter : (11, 2) and (-7,-4)

Answer 1

The form of the equation of the circle is

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

Where (h, k) are the coordinates of the center

r is the radius

Since the endpoints of the diameter are (11, 2) and (-7, -4), then

The center of the circle is the midpoint of the diameter

`\begin{gathered} M=((11+(-7))/(2),(2+(-4))/(2)) \\ M=((4)/(2),(-2)/(2)) \\ M=(2,-1) \end{gathered}`

The center of the circle is (2, -1), then

h = 2 and k = -1

Now we need to find the length of the radius, then

We will use the rule of the distance between the center (2, -1) and one of the endpoints of the diameter we will take (11, 2)

`\begin{gathered} r=\sqrt[]{(11-2)^2+(2--1)^2} \\ r=\sqrt[]{9^2+3}^2 \\ r=\sqrt[]{81+9} \\ r=\sqrt[]{90} \\ r^2=90 \end{gathered}`

Now substitute them in the rule above