The equation of a circle is given below.
$$
(x-5.2)^{2}+(y+3.7)^{2}=49
$$

What is its center?
$\square$ , $\square$
What is its radius?
If necessary, round your answer to two decimal places.
$\square$ units

Question

The equation of a circle is given below.
$$
(x-5.2)^{2}+(y+3.7)^{2}=49
$$

What is its center?
$\square$ , $\square$
What is its radius?
If necessary, round your answer to two decimal places.
$\square$ units

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the standard form of the circle's equation. ‖ ‖ step 2 ⋮ The given equation is $(x - 5.2)^2 + (y + 3.7)^2 = 49$. ‖ ‖ step 3 ⋮ The standard form of a circle's equation is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius. ‖ ‖ step 4 ⋮ Compare the given equation to the standard form to find the center $(h, k)$. ‖ ‖ step 5 ⋮ The center is $(5.2, -3.7)$. ‖ ‖ step 6 ⋮ To find the radius $r$, take the square root of the right side of the equation. ‖ ‖ step 7 ⋮ The radius is $\sqrt{49} = 7$ units. ‖ ∻1 Answer∻ ⚹ The center of the circle is $(5.2, -3.7)$ and the radius is $7$ units. ⚹ ∻Key Concept∻ ⚹Identifying the center and radius of a circle from its equation in standard form⚹ ∻Explanation∻ ⚹The center $(h, k)$ is found by comparing the given equation to the standard form and identifying the values of $h$ and $k$. The radius $r$ is the square root of the value on the right side of the equation.◊What is the equation of a circle given its center $(h,k)$ and radius $r$?⍭ Generate me a similar question◊⚹

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