Question

Find the center and radius of this

Answer 1

Answer:

Center = (7, -4)

Radius = 7

Step-by-step 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.

Answer 2

$\text{Hello there! :)}$

Answer:

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

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

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

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

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

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