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Common Core: High School - Geometry : Derive Circle Equation: CCSS.Math.Content.HSG-GPE.A.1

Study concepts, example questions & explanations for Common Core: High School - Geometry

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Example Questions

Example Question #11 : Derive Circle Equation: Ccss.Math.Content.Hsg Gpe.A.1

What is the equation of the circle shown below?

Plot11

Possible Answers:

$\left(x + 2\right)^{2} + \left(y - 5\right)^{2} = 6$

$\left(x - 2\right)^{2} + \left(y + 5\right)^{2} = 36$

$\left(x - 2\right)^{2} + \left(y - 5\right)^{2} = 36$

$\left(x + 2\right)^{2} + \left(y + 5\right)^{2} = 6$

$\left(x + 2\right)^{2} + \left(y + 5\right)^{2} = 36$

Correct answer:

$\left(x + 2\right)^{2} + \left(y + 5\right)^{2} = 36$

Explanation:

In order to find the equation, we must find the coordinates of the center of the circle.

If we look at the picture,

Plot11

we can see that the center is at $\left ( -2, -5\right )$

The next step it to find the radius. From looking at the picture, we can see that the radius is 6. With this information, we can plug it into the general circle equation.

The general circle equation is

$\left(- a + x\right)^{2} + \left(- b + y\right)^{2} = c^{2}$

Now we substitute for $\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$

We plug in the values, we get

$\left(x + 2\right)^{2} + \left(y + 5\right)^{2} = 36$

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Example Question #12 : Expressing Geometric Properties With Equations

What is the equation of the circle shown below?

Plot12

Possible Answers:

$\left(x - 2\right)^{2} + \left(y - 2\right)^{2} = 4$

$\left(x + 2\right)^{2} + \left(y - 2\right)^{2} = 2$

$\left(x + 2\right)^{2} + \left(y + 2\right)^{2} = 2$

$\left(x - 2\right)^{2} + \left(y + 2\right)^{2} = 4$

$\left(x + 2\right)^{2} + \left(y - 2\right)^{2} = 4$

Correct answer:

$\left(x + 2\right)^{2} + \left(y - 2\right)^{2} = 4$

Explanation:

In order to find the equation, we must find the coordinates of the center of the circle.

If we look at the picture,
Plot12
we can see that the center is at $\left ( -2, 2\right )$ .

The next step it to find the radius. From looking at the picture, we can see that the radius is 2.

With this information, we can plug it into the general circle equation.

The general circle equation is

$\left(- a + x\right)^{2} + \left(- b + y\right)^{2} = c^{2}$

Now we substitute for $\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$
We plug in the values, we get

$\left(x + 2\right)^{2} + \left(y - 2\right)^{2} = 4$

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Common Core: High School - Geometry : Derive Circle Equation: CCSS.Math.Content.HSG-GPE.A.1

Study concepts, example questions & explanations for Common Core: High School - Geometry

All Common Core: High School - Geometry Resources

Example Questions

Example Question #11 : Derive Circle Equation: Ccss.Math.Content.Hsg Gpe.A.1

Example Question #12 : Expressing Geometric Properties With Equations

All Common Core: High School - Geometry Resources

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