Question

55 Points

Find the center and radius, then write the standard equation of each circle

Answer 1

First circle has a center of (0,0) and a radius of 5

(x – 0) ^2 + (y – 0) ^2 = 5^2 or x^2 +y^2 = 25

The second circle has a center of (5, 4). The radius is 3.

(x – 5) ^2 + (y – 4) ^2 = 9

The last circle has a center of (4, 3) and a radius of 5.

(x – 4) ^2 + (y – 3) ^2 = 25

Answer 2

The standard form form for a circle is
`(x-h)^2+(y-k)^2=r^2`, where h and k are the center's coordinates respectively, and r is the radius. The first circle has a center at the origin, so the center's coordinates are (0, 0). Counting from the center straight across or up or down to a point on the circle tells us that the radius is 5. Our equation then is
`(x-0)^2+(y-0)^2=5^2`, or simplifying,
`x^(2) +y^2=25`. The second circle has a center of (5, 4). The radius is 3. So the equation for that circle is
`(x-5)^2+(y-4)^2=9`. The last circle has a center of (4, 3) and a radius of 5. The equation for that circle is
`(x-4)^2+(y-3)^2=25`. And there you go!