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4 votes
Find the center and radius of this

circle:
(x – 7)2+(y + 4)2= 49
Center = ([ ? 1,1])
Radius = [

2 Answers

3 votes

Answer:

Center = (7, -4)

Radius = 7

Explanation:

The general equation of a circle is:


(x-h)^(2)+(y-k)^(2)=r^(2)

where (h, k) is the center of the circle and r is the radius.

The equation given is in the form of the general equation of a circle. Knowing this, we will be able to find the center and radius by finding h, k, and r.


(x-7)^(2)+(y+4)^(2)=49

We can turn the 49 into 7² (√49 = 7, so 49 = 7²) and turn the equation into:


(x-7)^(2)+(y+4)^(2)=7^(2)

Now we can see that:

h = 7

k = -4

r = 7

So the center of the circle would be (7, -4) and the radius would be 7.

I hope you find my answer helpful.

User Smbd Uknow
by
7.9k points
7 votes


\text{Hello there! :)}

Answer:


\boxed{\text{Center at } (7, -4), \text{ Radius of } 7.}


\text{Formula for a circle: } (x - h)^(2) + (y - k)^(2) = r^(2) \text{ Where:}


h = \text{ x-coordinate of center}\\\\k = \text{ y-coordinate of center}\\\\r = \text{ radius}\\\\\text{Therefore:}


\text{In the equation } (x - 7)^(2) + (y + 4)^(2) = 49:


h = 7\\\\k = -4\\\\r = \sqrt[]{49} = 7 \\\\\text{So:}


\text{Center at } (7, -4), \text{ Radius of } 7.

User Oskenso Kashi
by
7.8k points

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