Question

Write the standard equation of a circle that passes through (-2, 10) with center (-2, 6)

Answer 1

is it a graph??????????

Answer 2

By definition, the standard equation of the circle is given by:

`(x-xo) ^ 2 + (y-yo) ^ 2 = r ^ 2`
Where,
(xo, yo): coordinates of the center of the circle
r: radius of the circle
To find the radius of the circle, we use the formula of distance between points.
We have then:

`r=√((x2-x1)^2+(y2-y1)^2)`
Substituting values:

`r=√((-2-(-2))^2+(6-10)^2)`

`r=√((-2+2)^2+(-4)^2)`

`r=√((0)^2+16)`

`r=√((0+16)`

`r=√((16)`

`r=4`
Then, the center of the circle is:

`(xo, yo) = (-2, 6)`
Substituting values in the general equation we have:

`(x-(-2))^2+(y-6)^2=4^2`
Rewriting:

`(x+2)^2+(y-6)^2=16`
Answer:
The standard equation of the circle is:

`(x+2)^2+(y-6)^2=16`