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High School Math : How to find the equation of a circle

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Example Question #1 : How To Find The Equation Of A Circle

The center of a circle is (2, 4) and its radius is . Which of the following could be the equation of the circle?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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Example Question #93 : Algebra I

Which one of these equations accurately describes a circle with a center of (2,3) and a radius of ?

Possible Answers:

x^2+y^2=25

(x-2)^2+(y-3)^2-25=0

(x^2+4)-(y^2+9)=25

(x-3)^2+(y-2)^2=25

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

Correct answer:

(x-2)^2+(y-3)^2-25=0

Explanation:

The standard formula for a circle is (x-a)^2+(y-b)^2=r^2 , with (a,b) the center of the circle and the radius.

Plug in our given information.

(x-a)^2+(y-b^2)=r^2

(x-2)^2+(y-3)^2=25

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

(x-2)^2+(y-3)^2-25=0

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High School Math : How to find the equation of a circle

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : How To Find The Equation Of A Circle

Example Question #93 : Algebra I

All High School Math Resources

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