Question

question 24, 2.4.45
match the graph with the correct equation.
xmin = - 10, xmax = 10, xscl = 1
ymin = - 10, ymax = 10, yscl = 1
the equation that matches the graph is
(x + 1)^2+(y - 2)^2 = 4.
(x - 1)^2+(y + 2)^2 = 4.
(x + 1)^2+(y + 2)^2 = 4.
(x - 1)^2+(y - 2)^2 = 4.

Explanation:

Step1: Recall circle - equation form

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

Step2: Identify center and radius from graph

By observing the graph, if we assume the center of the circle is at the point $(1, - 2)$ and the radius $r = 2$ (since $r^2=4$). Substituting $h = 1$, $k=-2$ into the standard - form equation, we get $(x - 1)^2+(y+2)^2=4$.

Answer:

$(x - 1)^2+(y + 2)^2=4$