Answer:
[tex](x-4)^2+(y+5)^2=4[/tex]
Step-by-step explanation:
We are given a circle with a radius of 2 with a center at the point (4, -5).
Assuming x and y to be the coordinates of any point on the circle, we can find the equation of the circle by using the following distance formula:
[tex]r=\sqrt{(x_1-x)^2+(y_1-y)^2}[/tex]
Putting the given values to get:
[tex]2=\sqrt{(x-4)^2+(y+5)^2}[/tex]
Taking square on both sides to get:
[tex]4=(x-4)^2+(y+5)^2[/tex]
Therefore, the equation of the given circle with radius 2 and center at (4, -5) is [tex](x-4)^2+(y+5)^2=4[/tex].
