Question

Math

Posted 5 months ago

```
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
```

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Answer from Sia

Verified answer

Posted 5 months ago

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.

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