Question

Find the equation of a circle with center $(0,0)$ and radius $5$.

• A. $x^2+y^2=5$
• B. $x^2-y^2=25$
• C. $x^2+y^2=25$
• D. $(x-1{)}^2+(y+1{)}^2=25$

Answer 1

The correct option is C $x^2+y^2=25$

Compare the equation with the standard form with center at $(h,k)$ and radius $r$ is: $(x-h{)}^2+(y-k{)}^2=r^2$
Substitute the value of $(h,k)=(0,0)$ and $r=5$
Then, the equation becomes $x^2+y^2=25$