Question

The circle below is centered at the origin, and the length of its radius is 7. What is the circle's equation. A. 7x+7y=49. B. x^2+y^2=49. C. x^2+y^2=14.

Answer 1

The equation of a circle is
`x^(2) + y ^(2) = 49` .

Option (B) is correct .

Explanation:

The general equation of a circle is given by

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

Where (h,k) are the centre of the circle r is the radius of a circle.

As given

The circle is centered at the origin, and the length of its radius is 7.

(h,k) = (0,0)

r² = 49

Put in the equation of a circle.

`(x - 0)^(2) + (y - 0)^(2) = 49`

`x^(2) + y ^(2) = 49`

Therefore the equation of a circle is
`x^(2) + y ^(2) = 49` .

Option (B) is correct .

Answer 2

Equation of a circle is: (x−h)2+(y−k)2=r2 h is the x-coordinate of the center and k is the y-coordinate of the center. Even though the formula has minus signs, those are positive numbers. If there were plus signs in there, the numbers h and k would actually be negative. Now since you're centered at the origin, that means h and k are 0, so you'd just have this: x2+y2=r2 Now since your radius is 7, just square it and replace r^2 woth that value :)