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Doss [256]
3 years ago
8

Whats the radius for the circle? x^2+2x+y^2+4y-6=0

Mathematics
1 answer:
MAXImum [283]3 years ago
5 0

Answer:

r = \sqrt{11}

Step-by-step explanation:

So we need to complete the square for both parts of the equation

First though we can add the 6 to the other side so we have x² + 2x + y² + 4y = 6

So first we can complete the square for x² + 2x

To do so we need to use (\frac{b}{2} )^{2} to figure out the number we need to add to both sides

In this case our b is 2, so substituting this in we get (\frac{2}{2} )^{2} =(1)^{2} =1

Here we add 1 to both sides and now we have x² + 2x + 1 + y² + 4y = 6 + 1

Now we can follow the same steps to complete the square for y² + 4y

Here our b is 4, so substituting this in we get (\frac{4}{2} )^{2}=(2)^{2} =4

Now we add 4 to both sides and now we have x² + 2x + 1 + y² + 4y + 4 = 6 + 1 + 4

Now condensing everything we have (x + 1)² + (y + 2)² = 11

The formula for a circle is (x - h)² + (y - k)² = r²

In our equation we have r² = 11

To find the radius we need to take the square root of both sides \sqrt{r^{2}}  =\sqrt{11} to get r = \sqrt{11}

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