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

Answer:

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

Step-by-step 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.