Question

what is the radius of the circle with the equation (x - 1)^2+(y - 4)^2 = 49?
a. 5
b. 7
c. 4
d. 6
what is the center of the circle with the equation (x - 3)^2+(y + 2)^2 = 25?
a. (3,2)
b. (-3,-2)
c. (3,-2)
d. (-3,2)
what is the center of the circle described by the equation (x - 9)^2+(y + 10)^2 = 81?
a. (9,10)
b. (9,-10)
c. (-9,10)
d. (-9,-10)

Explanation:

Step1: Recall circle - equation formula

The standard form of a circle's equation is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle and $r$ is the radius.

Step2: Find the radius of the first circle

For the equation $(x - 1)^2+(y - 4)^2 = 49$, since $r^2=49$, then $r=\sqrt{49}=7$.

Step3: Find the center of the second circle

For the equation $(x - 3)^2+(y + 2)^2 = 25$, comparing with $(x - h)^2+(y - k)^2=r^2$, we have $h = 3$ and $k=-2$. So the center is $(3,-2)$.

Step4: Find the center of the third circle

For the equation $(x - 9)^2+(y + 10)^2 = 81$, comparing with $(x - h)^2+(y - k)^2=r^2$, we have $h = 9$ and $k=-10$. So the center is $(9,-10)$.

Answer:

1. b. 7
2. c. $(3,-2)$
3. b. $(9,-10)$