Question

This circle is centered at the origin, and the length of its radius is 4. what is the equation of the circle?

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Answer 1

Option D is the correct answer

`\orange {\bold {{x}^(2) + {y}^(2) = {4}^(2)}}`

Explanation:

Since, circle is centered at the origin, and the length of its radius is 4. So, the equation of the circle will be:

`{(x - 0)}^(2) + {(y - 0)}^(2) = {4}^(2) \\ \\\purple {\bold {{x}^(2) + {y}^(2) = {4}^(2)}}`

Answer 2

The equation of the circle with center at the origin and radius 4 is
`x^2 + y^2 = 16.`

The equation of a circle with center
`(h, k)` radius r is given by
`(x-h)^2 + (y-k)^2 = r^2`

In this case, the circle is centered at the origin
`(h=0, k=0)` adius is 4.

⇒
`x^2 + y^2 = 4^(2)`

⇒
`x^2 + y^2 = 16.`

Therefore, the equation of the circle is
`x^2 + y^2 = 16.`