Question

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

Answer 1

r =
`√(11)`

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
`((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
`((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
`((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)} =√(11)` to get r =
`√(11)`