Question

Assume a quarter, diameter 0.96 inches, is centered at the point (–2, 5), where each unit represents one inch. Write the equation of a circle that would precisely enclose the coin.

Answer 1

If the diameter of this circle is .96, then the radius is .48.  The h and k values of our center are (-2, 5), and the standard form of a circle is $(x-h)^2+(y-k)^2=r^2$.  We will fill in accordingly.  $(x-(-2))^2+(y-5)^2=.48^2$.  That simplifies to $(x+2)^2+(y-5)^2=.2304$.  That's the equation of the circle that will completely enclose the quarter.

Answer 2

To write the circle equation $(x-x_0)^2+(y-y_0)^2=r^2$ you should know the centre coordinates $(x_0,y_0)$ and radius r.
1. $x_0=-2 \\ y_0=5$ and $r= \frac{0.96}{2} =0.48$ in.
2. The circle equation is:
 $(x+2)^2+(y-5)^2=0.48^2 \\ (x+2)^2+(y-5)^2=0.2304$.