Question 8 of 10

What is the equation of a circle centered at the origin with a radius of 15?

A. [tex]x^2 + y^2 = 15[/tex]
B. [tex]x^3 + y^3 = 15[/tex]
C. [tex]x^3 + y^3 = 225[/tex]
D. [tex]x^2 + y^2 = 225[/tex]



Answer :

To determine the equation of a circle centered at the origin with a given radius, we'll use the standard form of the equation of a circle.

The general equation for a circle centered at the origin [tex]\((0,0)\)[/tex] with radius [tex]\(r\)[/tex] is given by:
[tex]\[ x^2 + y^2 = r^2 \][/tex]

Here, we know the radius [tex]\( r \)[/tex] is 15.

1. Begin by squaring the radius:
[tex]\[ r^2 = 15^2 \][/tex]
2. Calculate [tex]\( 15^2 \)[/tex]:
[tex]\[ 15^2 = 225 \][/tex]
3. Substitute this value back into the general equation:
[tex]\[ x^2 + y^2 = 225 \][/tex]

Thus, the equation of the circle with a radius of 15 centered at the origin is:
[tex]\[ x^2 + y^2 = 225 \][/tex]

Looking at the multiple-choice options, we find the correct answer is:

D. [tex]\( x^2 + y^2 = 225 \)[/tex]