Answer: Easy to illustrate, hard to explain!
#3 Center is (0,-3) Radius is 2
Step-by-step explanation:
For any circle the basic formula is [tex]x^{2} +y^{2} = r^{2}[/tex]
that means if you know the square root of the radius and you put that in for x, y has to be 0 or if you put it in for y, x has to be 0.
In #3, r^2 is 4, you know the square root is +2 or -2. That gives you the "x boundaries" for the graph. (The center will be half way between them, so 0)
When x is 2 you need y to equal 0, so figure y+3 =0, solve for y and that gives you y = -3. So you have coordinates for the center of the circle: (0,-3)
and the radius is the square root of the given 4 so the radius = 2
The graph is attached below. Click on the thumbnail to expand properly!
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#4 is a bit more complicated, but if you think one step at a time, not impossible!
The square of the radius is 25, you know the square root 5, -5
Either x or y has to equal 5 when the other one is 0.
Use those facts to solve for x and y in parentheses.
x+4=5, so x= -4 and y-1=5 so y = 1
Those give you your x and y coordinates for the center: (-4,1)
The radius is the square root of 25, so the radius is 5
The graph is below. Click on the attachment to expand properly!
