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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 10, 2024
 #1
avatar+1334 
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Combining all like terms and bringing all terms to one side, we get

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

 

Now, completing the square fot both x and y, we get

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

 

According to the equation of the circle,

we get \(r=\sqrt{\left(\frac{\sqrt{17}}{4}\right)^2}=\sqrt{17}/4\)

 

Thanks! :)

 Jun 11, 2024

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