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Question 1 of 10

This circle is centered at the origin, and the length of its radius is 2. What is the circle's equation?

A. [tex]x^2 + y^2 = 2[/tex]
B. [tex]x^4 + y^4 = 4[/tex]
C. [tex]x^2 + y = 2[/tex]
D. [tex]x^2 + y^2 = 4[/tex]

Sagot :

GinnyAnswer
To find the equation of a circle centered at the origin (0, 0) with a given radius, we use the general equation of a circle:

[tex]\[ x^2 + y^2 = r^2 \][/tex]

where \( r \) is the radius of the circle.

1. We are given that the radius \( r \) is 2.

2. Substitute \( r = 2 \) into the equation:

[tex]\[ x^2 + y^2 = 2^2 \][/tex]

3. Calculate \( 2^2 \):

[tex]\[ 2^2 = 4 \][/tex]

4. Therefore, the equation of the circle is:

[tex]\[ x^2 + y^2 = 4 \][/tex]

Let's match this result with the given options:

A. \( x^2 + y^2 = 2 \) — Incorrect
B. \( x^4 + y^4 = 4 \) — Incorrect
C. \( x^2 + y = 2 \) — Incorrect
D. \( x^2 + y^2 = 4 \) — Correct

Hence, the correct answer is:

D. [tex]\( x^2 + y^2 = 4 \)[/tex]
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