Question

write the standard form of the equation and the general form of the equation of the circle with radius r and center (h,k). then graph the circle. r = 2; (h,k)=(0,2) the standard form of the equation of this circle is x²+(y - 2)² = 4. the general form of the equation of this circle is . (simplify your answer.)

Explanation:

Step1: Expand the standard - form equation

The standard - form of the circle is $x^{2}+(y - 2)^{2}=4$. Expand $(y - 2)^{2}$ using the formula $(a - b)^{2}=a^{2}-2ab + b^{2}$, where $a = y$ and $b = 2$. So, $(y - 2)^{2}=y^{2}-4y + 4$. The equation becomes $x^{2}+y^{2}-4y + 4=4$.

Step2: Simplify to get the general form

Subtract 4 from both sides of the equation $x^{2}+y^{2}-4y + 4=4$. We get $x^{2}+y^{2}-4y=0$.

Answer:

$x^{2}+y^{2}-4y = 0$