How to find the equation of a circle

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Math › How to find the equation of a circle

Questions 1 - 2

1

The center of a circle is and its radius is . Which of the following could be the equation of the circle?

$(x - 2)^{2} + (y - 4)^{2} = 100$

$(x + 2)^{2} + (y + 4)^{2} = 100$

$(x - 2)^{2} + (y - 4)^{2} = 10$

$x^{2} + y^{2} = 100$

$2x^{2} + 4y^{2} = 100$

Explanation

The general equation of a circle is $(x - h)^{2} + (y - k)^{2} = r^{2}$ , where the center of the circle is and the radius is .

Thus, we plug the values given into the above equation to get $(x - 2)^{2} + (y - 4)^{2} = 100$ .

2

Which one of these equations accurately describes a circle with a center of and a radius of ?

$\sqrt{x^2+y^2-3^2-2^2}=5$

Explanation

The standard formula for a circle is , with the center of the circle and the radius.

Plug in our given information.

This describes what we are looking for. This equation is not one of the answer choices, however, so subtract from both sides.

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