Question

Which equation is an equation of a circle with a radius of 2 and its center is at (4, -2)? (x - 4)² + (y + 2)² = 4 (x - 4)² + (y + 2)² = 2 (x + 4)² + (y - 2)² = 4

Answer 1

(x - 4)² + (y + 2)² = 4

Explanation:

Answer 2

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

Explanation:

A circle is the set of all points on a plane at a given distance (radius) from a given point (center). The general equation of a circle with center
`(h,k)` and radius
`r` is given by:

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

Therefore, replacing the data provided into the previous equation:

`Center=(4,-2)=(h,k)\\\\h=4\\\\k=-2\\\\Radius=2\\\\r=2`

`(x-(4))^2+(y-(-2))^2=(2)^2\\\\(x-4)^2+(y+2)^2=4`

So, the equation of a circle with a radius of 2 and its center at (4,-2) is:

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

I attach you the graph.