Question

question 3 of 10

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

a. \\(x + y = 4\\)
b. \\(x^2 + y^2 = 4\\)
c. \\(x^6 + y^6 = 4\\)
d. \\(x^2 + y^2 = 16\\)

Explanation:

Identify the standard equation of a circle centered at the origin

$$ x^2 + y^2 = r^2 $$

Substitute the given radius value

$$
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$$

Write the final equation

$$ x^2 + y^2 = 16 $$

Answer:

• (A) \(x + y = 4\)
• (B) \(x^2 + y^2 = 4\)
• (C) \(x^6 + y^6 = 4\)
• (D) \(x^2 + y^2 = 16\) (Correct answer)