Question

Find the radius and write an equation of a circle that passes through (8,4) and (0,-2)

Answer 1

Given

A circles passes through A(8,4) and B(0,-2).

To find the radius and the equation of the circle.

Step-by-step explanation:

It is given that,

A circles passes through (8,4) and (0,-2).

Then, the diameter of the circle is,

`\begin{gathered} d=√((x_2-x_1)^2+(y_2-y_1)^2) \\ d=√((8-0)^2+(4-(-2))^2) \\ =√(8^2+(4+2)^2) \\ =√(8^2+6^2) \\ =√(64+36) \\ =√(100) \\ =10\text{ }units \end{gathered}`

Therefore, the radius of the circle is,

`\begin{gathered} r=(d)/(2) \\ =(10)/(2) \\ =5\text{ }units \end{gathered}`

Also, the center of the circle is,

`\begin{gathered} Midpoint\text{ }of\text{ }AB=((x_1+x_2)/(2),(y_1+y_2)/(2)) \\ =((8+0)/(2),(4+(-2))/(2)) \\ =((8)/(2),(2)/(2)) \\ =(4,1) \end{gathered}`

Therefore, the center is (4,1).

Now, consider the equation of the circle as,

`(x-4)^2+(y-1)^2=5^2`

That implies,