+441 The graph of the equation
4x^2 - 12x + 4y^2 + 16y + 17 = -4x + 2y + 5
is a circle. Find the radius of the circle.
+4 Start by moving all the terms to one side and combining like terms:
\(4x^2-8x+4y^2+14y+12=0\)
Then, divide both sides by \(4 \):
\(x^2-2x+y^2+\frac{7}{2}y+3=0\)
Next, complete the square for \(x \) and \(y \):
\((x-1)^2+(y+\frac{7}{4})^2-1-\frac{49}{16}+3=0\)
Simplify:
\((x-1)^2+(y+\frac{7}{4})^2=\frac{17}{16}\)
This is the equation (in standard form) for the circle. Now take the square root of \(\frac{17}{16} \):
\(\sqrt{\frac{17}{16}}=\frac{\sqrt{17}}{\sqrt{16}}=\boxed{\frac{\sqrt{17}}{4}}\) Which is our answer.
