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# Geometry

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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

#1
+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

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

$$\sqrt{17}/4$$

Thanks! :)

Jun 25, 2024

#1
+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

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

$$\sqrt{17}/4$$