Verified Answer :

meerkat18

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 :)

Answer:

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

Option (B) is correct .

Step-by-step 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 .

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