Find an equation for a circle satisfying the given conditions. (a) center (-1, 4), passes through (3, 7) (b) the points (7, 13) and (-3, -11) are at the ends of a diameter.

Step-by-step explanation:

In order to find the equations we need the circle's general equation:

where:

(h,k) is the center and 'r' is the radius.

A. Because the center is (-1,4) then h=-1 and k=4.

Now we can find the radius as:

so we have r=5

Then the equation is

B. Because we have two points defining a diameter we can find the radius as follows:

Now let's find the center of the circle as follows:

Then the equation is

domain is all the x values included in the

0 ≤ x ≤ 2

range is all the y values of the graph

-2 ≤ y ≤ 2

***keep in mind that there are different ways to show domain and range

hope this !

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step-by-step explanation: