Question

The coordinates at the end of

the diameter of a circle are
(3,0) and (-5,-4). Find the
equation of the circle.

Answer 1

`(x+1)^(2) +(y+2)^(2) =20`

Explanation:

Using the mid point formula to find the center of the circle:

midpoint =
`((x_(1) +x_(2) )/(2) ,(y_(1) +y_(2) )/(2) )`

Midpoint =
`((3+-5)/(2) ,(0+-4)/(2) )`

Midpoint =
`(-1,-2)`

The midpoint is the same as the centre of the circle

Find the distance(the diameter of the circle) between those two points to find the radius:

Distance formula =
`\sqrt{(y_(2)-y_(1) )^(2) +(x_(2) -x_(1) ) ^(2) }`

Distance formula =
`\sqrt{(-4-0)^(2) +(-5-3)^(2) }`

Distance formula =
`√(16+64)`

Distance formula =
`√(80)`

So,the diameter is
`√(80)` and to find the radius we need to divide the diameter by two

Radius =
`(√(80) )/(2)`

Radius =
`2√(5)`

the equation of circle:

Radius =
`2√(5)`

Center = (-1,-2)

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

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

`(x+1)^(2) +(y+2)^(2) =20`