The equation of a circle in general form is $$ x^{2}+y^{2}+6 x-4 y+4=0 $$ Write the equation in standard form. (1 point) $$ (x+3)^{2}+(y-2)^{2}=4 $$ $$ (x+3)^{2}+(y-2)^{2}=9 $$ $$ (x+3)^{2}+(y+2)^{2}=4 $$ $$ (x+3)^{2}+(y+2)^{2}=9 $$

The standard form of the given circle equation $$ x^{2}+y^{2}+6x-4y+4=0 $$ is: \[ (x+3)^{2} + (y-2)^{2} = 9 \] **Answer:** $$ (x+3)^{2}+(y-2)^{2}=9 $$ The standard form of the circle is $$ (x+3)^{2}+(y-2)^{2}=9 $$.

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The equation of a circle in general form is
Write the equation in standard form.
(1 point)

Ask by Perkins Fowler. in the United States

Jan 04,2025

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The standard form of the circle is

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Beyond the Answer

To convert the given equation of the circle from general form to standard form, you can complete the square for both

and

Starting with the equation

, rearranging gives us:

Next, complete the square for

Take half of 6 (which is 3), square it (gets 9), and add it:

Then, complete the square for

Take half of -4 (which is -2), square it (gets 4), and add it:

Incorporating these adjustments into the equation, it becomes:

Thus, the standard form of the circle’s equation is:

Now for the circle’s features: a circle’s radius is the square root of the number on the right side of the equation! In this case, the radius is 3, which can lead to fun activities like drawing a perfect circle with a compass!

And speaking of circles, did you know that circles have been a part of human history for thousands of years? Ancient civilizations, from the Babylonians to the Greeks, studied circles and developed the mathematical principles we still use today. The fascination with this shape is woven into our fabric, influencing art, architecture, and even science.

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