Question

given a circle with center (0, 0) and radius 2.2, (a) write an equation of the circle in standard form. (b) graph the circle. part 1 of 2 (a) an equation of the circle in standard form is. part 2 of 2 (b) graph the circle. try again

Explanation:

Step1: Recall standard circle equation

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

Step2: Substitute center $(0,0)$

Substitute $h=0$, $k=0$: $(x-0)^2+(y-0)^2=r^2$, simplifying to $x^2+y^2=r^2$.

Step3: Substitute radius $2.2$

Calculate $r^2$: $2.2^2 = 4.84$. Substitute to get $x^2+y^2=4.84$.

Step4: Describe graphing the circle

Plot center $(0,0)$, mark points 2.2 units up/down/left/right from center: $(2.2,0)$, $(-2.2,0)$, $(0,2.2)$, $(0,-2.2)$. Draw a smooth circle through these points.

Answer:

(a) $x^2 + y^2 = 4.84$
(b) To graph:

1. Plot the center at the origin $(0,0)$.
2. Plot four key points: $(2.2, 0)$, $(-2.2, 0)$, $(0, 2.2)$, $(0, -2.2)$.
3. Draw a smooth, closed circle passing through all four plotted points.