Question

Question #b6651

Answer 1

The equation is:

`(x-3)^2+(y-2)^2=(sqrt117)^2`

Explanation:

The standard Cartesian form for the equation of a circle is:

`(x-h)^2+(y-k)^2=r^2" [1]"`

where `(x,y)` is any point of the circle, `(h,k)` is the center point, and r is the radius.

Substitute the center `(3,2)` into equation [1]:

`(x-3)^2+(y-2)^2=r^2" [2]"`

Use equation [2] and the point `(-6,-4)`, to find the value of r:

`(-6-3)^2+(-4-2)^2=r^2`

`(-9)^2+(-6)^2=r^2`

`81+36=r^2`

`r^2 = 117`

`r = sqrt(117)`

The equation is:

`(x-3)^2+(y-2)^2=(sqrt117)^2" [3]"`

Answer 2

Use distance formula to find the radius.
`r = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`

`r = sqrt((-6 - 3)^2 + (-4 - 2)^2)`

`r = sqrt((-9)^2 + (-6)^2)`

`r = sqrt(81 + 36)`

`r = sqrt(117)`

Now plug into equation of a circle

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

`(x-3)^2 + (y-2)^2 =sqrt(117)^2`

`(x-3)^2 + (y-2)^2 =117`