Question

A Circle is centered at the point 5.4 and passes through the point 3.2 what is the equation?

Answer 1

`{(x - 5)}^(2) + {(y - 4)}^(2) = 8`

Explanation:

Equation of circle can be written as

`{(x - a)}^(2) + {(y - b)}^(2) = {r}^(2)`

Here,r is radius and (a,b) is center of circle.

Given that circle is passing through ( 3,2 ) and center is ( 5,4 )

we can calculate radius r as

`{r}^(2) = {( x_(1) - a)}^(2) + {( y_(1) - b)}^(2)`

`{r}^(2) = {( 3 - 5)}^(2) + {( 2 - 4)}^(2) \\ {r}^(2) = 4 + 4 \\ {r}^(2) = 8`

Replacing values in equation of circle.

thus,

`{(x - 5)}^(2) + {(y - 4)}^(2) = 8`