Question

Using the following equation,find the center and radius of the circle x^2 + 2x + y^2 +4y=20

Answer 1

Answer:

center of x²+2x+y²+4y=20:(-1,-2),r=5

Step-by-step explanation:

look at the attachment above ☝️

Answer 2

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: $(x-h)^2 +(y-k)^2 = r^2$

• (h,k): coordinates of the center
• r: length of the radius

        $x^2+2x+y^2 + 4y = 20$

       1. complete the square to get quadratic equation for 'x' and 'y'

        $x^2 + 2x + ..... + y^2 + 4y + .... = 20\\\rm\hookrightarrow x^2 + 2x + 1 + y^2 + 4y + 4=20 + 1 +4$

       2. Factorize the quadratics

       $x^2 + 2x + 1+ y^2 + 4y + 4 = 20 + 1 +4\\(x+1)(x+1) + (y+2)(y+2) = 25\\(x+1)^2 +(y+2)^2=5^2$

       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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