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Simora [160]
3 years ago
13

Find the center and radius of the circle with the given equation. Then select the correct graph of the equation.

Mathematics
1 answer:
likoan [24]3 years ago
3 0

Answer:

Step-by-step explanation:

In order to find the center and the radius of this circle, you have to complete the square on it. And only for the x-terms, because the y term is squared and there is no other y term. We'll get to that in a second.

Take half the linear x-term, square it and add it to both sides. Our linear term is 10. Half of 10 is 5, and 5 squared is 25. We add 25 to both sides:

The reason we do this is to create a perfect square binomial inside that set of parenthesis. Simplifying the right side as well gives us:

This tells us that the center is (-5, 0). Remember when I said we would get back to the y terms? Because there was only a y-squared and no other y terms, that is the same as writing the equation as

The radius is the square root of the constant. So the radius is 6.

D is the graph you want.

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We know by definition that complementary angles add up to 90 degrees. We can set up an equation using the ration given:

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We now know that the number we multiply the ratio by is 3. The smaller number in the ratio is 13, and so therefore we multiply it by 3.

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