Question

write the standard form of the equation and the general form of the equation of the circle of radius r = 4 and center (h,k)=(0,0). graph the circle. the standard form of the equation of this circle is x^{2}+y^{2}=16. the general form of the equation of this circle is x^{2}+y^{2}-16 = 0. (simplify your answer.) use the graphing tool to graph a circle with center (0,0) and a radius of 4. click to enlarge graph

Explanation:

Step1: Recall circle standard - form formula

The standard - form of the equation of a circle with center $(h,k)$ and radius $r$ is $(x - h)^2+(y - k)^2=r^2$.

Step2: Substitute given values

Given $h = 0,k = 0,r = 4$, we substitute into the formula: $(x-0)^2+(y - 0)^2=4^2$, which simplifies to $x^{2}+y^{2}=16$.

Step3: Convert to general form

The general form of a circle equation is $x^{2}+y^{2}+Dx + Ey+F = 0$. Starting from $x^{2}+y^{2}=16$, we subtract 16 from both sides to get $x^{2}+y^{2}-16 = 0$.

Answer:

Standard form: $x^{2}+y^{2}=16$
General form: $x^{2}+y^{2}-16 = 0$