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Equation of the circle

Equation of the circle-example-1
User Lisa Wray
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1 Answer

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Answer:

(x + 3)^2 + (y - 4)^2 = 5

Explanation:

Note that the center is the midpoint of the diameter. Use the midpoint formula to find the coordinates of the center:

-8 + 2

x0 = ----------- = -3

2

6 + 2

y0 = ----------- = 4

2

The center of this circle is (-3, 4).

Thus, the equation of this circle is (x + 3)^2 + (y - 4)^2 = r^2.

Find r by substituting the coordinates of one of the diameter endpoints into the above equation:

(-2 + 3)^2 + (6 - 4)^2 = r^2, or

1 + 4 = r^2 = 5. Thus, the radius is √5.

The fourth answer choice best corresponds with the above result.

The equation of the circle is either the generic (x + 3)^2 + (y - 4)^2 = r^2 or the specific (x + 3)^2 + (y - 4)^2 = 5.

User Weez
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7.3k points