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The graph of the equation
4x^2 - 12x + 4y^2 + 16y + 17 = -4x + 2y + 5
is a circle. Find the radius of the circle.

 Jun 25, 2024

Best Answer 

 #1
avatar+1230 
+1

The formula of a circle is in the form of

\(\left(x−a\right)^2+\left(y−b\right)^2=r^2\) where (a,b) is the center and r is the radius. 

 

First, let's move all the terms to one side. We get

\(4x^2-8x+4y^2+14y-12=0\)

 

Dividing everything by 4, we have

\(x^2-2x+y^2+7/2y-3=0\)

 

Completing the square for both x and y, we have

\(\left(x-1\right)^2+\left(y-\left(-\frac{7}{4}\right)\right)^2=\left(\frac{\sqrt{17}}{4}\right)^2\)

 

Thus, the radius is just 

\(\sqrt{17}/4\)

 

Thanks! :)

 Jun 25, 2024
 #1
avatar+1230 
+1
Best Answer

The formula of a circle is in the form of

\(\left(x−a\right)^2+\left(y−b\right)^2=r^2\) where (a,b) is the center and r is the radius. 

 

First, let's move all the terms to one side. We get

\(4x^2-8x+4y^2+14y-12=0\)

 

Dividing everything by 4, we have

\(x^2-2x+y^2+7/2y-3=0\)

 

Completing the square for both x and y, we have

\(\left(x-1\right)^2+\left(y-\left(-\frac{7}{4}\right)\right)^2=\left(\frac{\sqrt{17}}{4}\right)^2\)

 

Thus, the radius is just 

\(\sqrt{17}/4\)

 

Thanks! :)

NotThatSmart Jun 25, 2024

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