+631 The graph of the equation
4x^2 - 12x + 4y^2 + 16y + 17 = -4x + 2y + 5
is a circle. Find the radius of the circle.
+1926 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! :)
+1926 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! :)
