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This circle is centered at the point (2,6), and the length of its radius is 4. What
is the equation of the circle?
O A. (x-6)2 + (x - 2)2 = 16
O B. (x²-2) + (7-6) = 4²
O C. (x - 2)2 + (-6)2 = 16
O D. (x + 2)2 + (x + 5)2 = 4

Respuesta :

Option C: [tex](x-2)^2+(y-6)^2=16[/tex] is the equation of the circle.

Explanation:

Given that the circle is centered at the point [tex](2,6)[/tex] and the length of its radius is 4.

We need to determine the equation of the circle.

The equation of the circle with center [tex](h,k)[/tex] and radius r is given by the equation,

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Substituting the center and the radius in the above formula, we get,

[tex](x-2)^2+(y-6)^2=4^2[/tex]

Simplifying the radius, we get,

[tex](x-2)^2+(y-6)^2=16[/tex]

Thus, the equation of the circle is [tex](x-2)^2+(y-6)^2=16[/tex]

Hence, Option C is the correct answer.

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