Question

Find the equation of a circle with the same center as the circle in the graph above and that passes through a point 2 units away from the given circle.

Answer 1

The equation of a circle with center at (a, b) and radius, r, is given by
$(x-a)^2+(y-b)^2=r^2$

The given circle in the graph has the center at (0, 2) with the radius of 1 units.

A circle with the same center as the circle in the graph and that passes through a point 2 units away from the given circle has its center at (0, 2) and a radius of 3 units.

Thus the equation of the circle is given by
$(x-0)^2+(y-2)^2=3^2 \\ \\ x^2+y^2-4y+4=9 \\ \\ x^2+y^2-4y-5=0$