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

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= (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`.

Answer 2

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.