Find the center (h,k) and radius r of the circle: 5x^2+10x+5y^2=0

embizze | High School Teacher | (Level 1) Educator Emeritus

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Given `5x^2+10x+5y^2=0` ; Find the radius and center of the circle:

`5x^2+10x+5y^2=0`

`5(x^2+2x+y^2)=0`

`5(x^2+2x+1-1+y^2)=0` **Complete the square on `x^2+2x`

`5((x+1)^2+y^2)-5=0`

`(x+1)^2+y^2=1`

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Center is at (-1,0) with a radius of 1

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** Checking -- write the original as an explicit function:

`5x^2+10x+5y^2=0`

`5y^2=-5x^2-10x`

`y^2=-x^2-2x`

`y=+-sqrt(-x^2-2x)`

The graph of these two functions:

The graph of `y=+-sqrt(1-(x+1)^2)` :

justaguide | College Teacher | (Level 2) Distinguished Educator

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The center and radius of the circle 5x^2+10x+5y^2=0 has to be determined.

5x^2+2x+5y^2=0

=> x^2 + 2x + 1 + y^2 = 1

=> (x + 1)^2 + (y - 0)^2 = 1^2

This is in the form (x - h)^2 + (y - k)^2 = r^2 where the center is (h, k) and the radius is r.

The center of the circle is (-1, 0) and the radius is 1