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Resources

Convert equations of circles from general to standard form

In the figure below

AD

is tangent to circle

O

D

AD=15

BC=16

AB

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x^{(@)}=25\quad x=53

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252

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Find the following measures for the circle above:

A circle is touching the side

P Q

\triangle A P Q

E

and touching the side

A P

A Q

B

C

respectively. If

A B=5 \mathrm{~cm}

, then find the perimeter of

\triangle A P Q

uation of the circle is

x^{2}+18 x+y^{2}-12 y-27=0

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the standard form equation of a circle. Show your reasoning.

5

The equation of a circle is shown.

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x^{2}+y^{2}-10 x+8 y+16=0

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What is the radius of the circle?

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A circle in the

xy

-plane has the equation

4x^2+4y^2-24x=28

. What is the diameter of the circle?

Using the formula for the surface of a hemisphere

A = 3\pi r^2

, what is the radius of the sphere if the area is

18.75\pi\,\text{cm}^2

(x + 4)^2 + (y - 19)^2 = 121

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The graph of the given equation is a circle in the

xy

-plane. The point

(a, b)

lies on the circle. Which of the following is a possible value for

a

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-16

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-14

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11

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19

The circle has center

O

, and the measure of angle

\angle POQ

45\%

. The length of minor arc

AC

is what fraction of the circumference of the circle? The number of degrees of arc in a circle is

360

A circle in the xy-plane has the equation

(x-0.8)^2+(y-5.2)^2=1.69

. How long is the radius of the circle?

A circle in the XY-plane has the equation

(x-0.8)^2 + (y-5.2)^2=1.69

. How long is the radius of the circle?

B

with a radius of

5

units is shown on a coordinate grid. Circle

B

is dilated by a scale factor of

\frac{7}{5}

, centered at the origin, to map to Circle

M

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Complete the statement.

A cube is pictured below. Select the type of cross section formed when the figure is cut parallel to its base.

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A circle in the xy-plane has the equation

x^{2}+y^{2} -10x+32y+272=0.

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Which of the following best describes the location of the center of the circle and the length of its radius?

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1

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(10,-32)

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4\sqrt{17}

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(-10,32)

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4\sqrt{17}

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(-5,16)

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3

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(5,-16)

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3

Write the equation in standard form for the circle

x^2+y^2-6y-9= 0

Write the equation in standard form for the circle

x^2+y^2+10y-25= 0

Write the equation in standard form for the circle

x^2+y^2-16= 0

Write the equation in standard form for the circle

x^2+y^2-4x+7= 0

Write the equation in standard form for the circle

x^2+y^2+6x-1= 0

Write the equation in standard form for the circle

x^2+y^2-9=0

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