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The distance between the midpoint and the circle border is called the radius. First we need to find the angle for each piece, since we know that a full circle is.
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How to see a full circle rainbow | Earth | EarthSky
Hear from a master of sky optics. This double rainbow was captured in Wrangell-St.
Elias National Park, Alaska. Photo via Eric Rolph at Wikimedia Commons.
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Rearrange the terms if needed. First we needto move the constant -4 to the other side: The coefficient of x is We need to take that number, divide it by 2 and square it.
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We'll want to add it by the -2x term to create a trinomial: Now we'll factor the trinomial shown in green If we did everything correctly, factoring should always produce a perfect square. Let's rewrite it: Now we'll repeat the process for the y.
We start by finding the coefficient of the first degree term, which is We divide it by 2 then square it. We'll add this to both sides: Next we factor the trinomial: And rewrite it: This matches our pattern, so this is our final answer: We would now be able to easily find the center and radius.
First we want to move the constant -3 to the other side: The coefficient of xis We'll want to put it by the -6x term to create a trinomial: Now we'll factor the trinomial shown in green If we did everything correctly, factoring should always produce a perfect square.