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Using the following equation,find the center and radius of the circle

x^2 + 2x + y^2 +4y=20

Sagot :

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Answer:

center of x²+2x+y²+4y=20:(-1,-2),r=5

Step-by-step explanation:

look at the attachment above ☝️

View image Cygnusabc00
Linandrew41idn

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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