IXL - Write equations of circles in standard form from graphs (Geometry practice)

Write the equation of this circle in standard form.

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question

Write the equation of this circle in standard form.

key idea

A circle is the set of points in a plane that are the same distance from a fixed point. The distance is the

radius.

The point is the

center.

The equation of a circle in standard form is

(

–

)

(

–

)

The center is

(

)

The radius is

The origin is (0, 0).

solution

Look at the graph of the circle:

The center is

(

)

which is the origin.

To find the radius, locate a point on the circle. Calculate the distance between the center and that point.

Locate a point on the circle.

Look at the graph:

(

)

is a point on the circle.

Calculate the distance.

Since

(

)

and

(

)

have the same

-coordinate,

0, the distance between them is the absolute value of the difference in their

-coordinates:

–

The radius is 5.

Write the equation in standard form.

The equation of the circle in standard form is:

(

–

)

(

–

)

(

–

)

(

–

)

Plug in

and

Plug in

and

Looking for more? Try these:

Lesson: Equations of circles

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Work it out

Not feeling ready yet? These can help:

Y.4Derive equations of circles using the Pythagorean theorem

Y.3Determine if a point lies on a circle

Lesson: Equations of circles

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