The equation of a circle is (x+3)^(2)+(y-4)^(2)=49. What are the center and radius of the circle? Choose 1 answer: (A) The center is (3,4) and the radius is 7 . (B) The center is (-3,4) and the radius is 7 . (c) The center is (-3,-4) and the radius is 7 . (D) The center is (-3,4) and the radius is 49 .

Question

The equation of a circle is  (x+3)^(2)+(y-4)^(2)=49. What are the center and radius of the circle? Choose 1 answer: (A) The center is  (3,4) and the radius is 7 . (B) The center is  (-3,4) and the radius is 7 . (c) The center is  (-3,-4) and the radius is 7 . (D) The center is  (-3,4) and the radius is 49 .

Bytelearn · Accepted Answer

Equation of a Circle: The equation of a circle in standard form is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center of the circle and $r$ is the radius. We need to compare the given equation $(x+3)^2 + (y-4)^2 = 49$ with the standard form to find the center and the radius.Finding the Center: The given equation is already in standard form. To find the center $(h, k)$, we look at the signs in front of the numbers inside the parentheses. The center will be $(-3, 4)$ because the equation has $(x+3)$ and $(y-4)$, which means $h = -3$ and $k = 4$.Finding the Radius: To find the radius $r$, we take the square root of the number on the right side of the equation. The square root of $49$ is $7$, so the radius of the circle is $7$.Matching the Information: Now we have the center $(-3, 4)$ and the radius $7$. We can match this information with the answer choices.

Full solution

More problems from Solve polynomial equations

Related topics