Question

question 5 of 25

which of the following equations correctly represents a circle centered at the origin with a radius of 5?

a. \\((x - 5)^2 + (y - 5)^2 = 5\\)
b. \\(x^2 + y^2 = 25\\)
c. \\(x^2 + y^2 = 5\\)
d. \\((x - 5)^2 + y^2 = 25\\)

Explanation:

Identify the standard form of a circle centered at the origin

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

Substitute the given radius into the equation

$$
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$$

Match the resulting equation with the options

$$ \text{Option B: } x^2 + y^2 = 25 $$

Answer:

• (A) \((x - 5)^2 + (y - 5)^2 = 5\)
• (B) \(x^2 + y^2 = 25\) (Correct answer)
• (C) \(x^2 + y^2 = 5\)
• (D) \((x - 5)^2 + y^2 = 25\)