A circle’s standard form of an equation is:
(x-h)^2 + (y-k)^2 = radius^2
Plug in h and k immediately because that is something you automatically know. H and k are derived from the center of the circle. The center of the circle is (h,k). Don’t get tripped up though, your center of a circle has negative coordinates. When you have two negatives, they become positive.
So now you have:
(x+4)^2 + (y-2)^2 = radius^2
So figure out what the radius is. Use the distance formula to find out. You have a change of 5 from -4 to 1 in x. You have a change of 2 from 2 to 4 in y. Distance formula has the distance as the square root of x distance squared and y distance squared. That would mean that the distance/radius is equal to the square root of (25 + 4). 5 squared is 25 while 2 squared is 4.
The radius of the circle is equal to the square root of (29). However, looking back at the circle equation the radius should be squared for the equation. Square root of 29 squared gets you 29.
Plug that in and you get:
(x+4)^2 + (y-2)^2 = 29
Do you know that multiplicity means the number of times any factor appears in the factored result? Just checking. For example The graph of y = x^2 - 2x + 1 has a multiplicity of 2. they are y = (x - 1) * ( x - 1)
y = x^2 - 3x - 4 has 2 factors.
y = (x - 4)(x + 1) each of the factors has a multiplicity of 1.
So the answer to your question is there are 5 real zeros and 2 complex zeros.
Okay, so since both y values share the same number, let's add both equations so the y values cancel out leaving us to solve for x.
10x+(-5x)=5x
7y+(-7y)=0
1+24=25
Now we have 5x=25
divide both sides by 5 and we have x=5
Now that we know x=5, we can plug it into one of the problems to find y.
Let's do 10(5) +7y=1
50+7y=1 subtract 5 and we get 7y=-49
divide -7 from both sides and we get y=-7
so there you have it x=5 and y=-7
It is the same thing as the average you add everything up then you divide by the number of numbers you added together
