SOLUTION: could anyone help me with these two questions? 1. Is the graph of a circle a graph of a function? (Yes or no) 2. Find the center and the radius of the circle represented by t

Question 145089: could anyone help me with these two questions?
1. Is the graph of a circle a graph of a function? (Yes or no)
2. Find the center and the radius of the circle represented by the equation
x2 + y2 + 10x � 4y � 7 = 0

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
1) The answer is NO! You can check this by using the "vertical line test" in which you draw a vertical line through the circle on the graph containing the circle.
If the vertical line passes through the graph (circle) only once, then the graph is a function. In the case of a circle, the vertical line would pass through the graph (circle) twice, so the equation represented by the graph is not a function.
2) Find the center and the radius of the circle represented by the equation:

The goal is to transform this equation into the standard form of the equation for a circle with center at (h, k) and radius r, . First, add 7 to both sides of the equation.
Now group the x-terms together and the y-terms together.
The next step is to "complete the square" in both the x-terms and the y-terms. You do this by adding the square of half the x-coefficient: () and likewise for the y-coefficient () to both sides of the equation.
Now factor the x- and y-groups and simplify.
Compare this with the standard form
You can see that h = -5, k = 2, and
So, the center is at (h,k) = (-5,2) and the radius, = 6.

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