Question

graph the circle with equation (x + 1)^2+(y - 2)^2 = 25. plot the center and then a point on the circle. -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 0 1 2 3 4 5 clear all draw: question help: video written example message instructor submit question

Explanation:

Step1: Identify circle - center formula

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

Step2: Determine the center

For the equation $(x + 1)^2+(y - 2)^2=25$, we have $h=-1$ and $k = 2$. So the center is $(-1,2)$.

Step3: Determine the radius

Since $r^2 = 25$, then $r = 5$.

Step4: Find a point on the circle

Starting from the center $(-1,2)$, if we move 5 units to the right (increase $x$ - value by 5), a point on the circle is $(-1+5,2)=(4,2)$.

Answer:

Center: $(-1,2)$; Point on the circle: $(4,2)$