Let's take this problem step by step:
Let's try to put what we have into the standard equation form of a circle
⇒ standard form: [tex](x-h)^2 +(y-k)^2 = r^2[/tex]
- (h,k): coordinates of the center
- r: length of the radius
[tex]x^2+2x+y^2 + 4y = 20[/tex]
1. complete the square to get quadratic equation for 'x' and 'y'
[tex]x^2 + 2x + ..... + y^2 + 4y + .... = 20\\\rm\hookrightarrow x^2 + 2x + 1 + y^2 + 4y + 4=20 + 1 +4[/tex]
2. Factorize the quadratics
[tex]x^2 + 2x + 1+ y^2 + 4y + 4 = 20 + 1 +4\\(x+1)(x+1) + (y+2)(y+2) = 25\\(x+1)^2 +(y+2)^2=5^2[/tex]
3. Based on the last equation
⇒ we see the standard equation of the circle
Now let's collect the information needed:
Answer:
- Center: (-1, -2)
- Radius: 5
Hope that helps!
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