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Given the equation of a circle:
Find its center and radius. Sketch the graph.
Solution:
From the given equation,
This equation represents a circle because the coefficients of x2 and y2 are the same and no xy term in the general equation of a conic section. Circle is also a type of conic section. Our goal right now is to find its center and radius. Since x2 and y2 have their coefficients, we have to divide both sides of the equation by 4 in order to eliminate their coefficients, we have
Group the above equation according to their variables and transpose the coefficient to the right side of the equation,
Next, let's do the completing the square for x2 and y2,
The above equation can be written as
In order to get the center and radius of a circle, the equation must be simplified into standard form. The above equation is now in standard form.
To get the center of a circle,
x - 1 = 0 y + 2 = 0
x = 1 y = -2
Therefore, C(1, -2)
The radius of a circle is 3.
We can now sketch the graph using the above results.
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| Photo by Math Principles in Everyday Life |