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Sophie D.

Point-sloe form of an equation

m=Y2-Y1/X2-X1

Point slope form is: (found by cross mulitiplying)

y-y1=m(x-x1)

distance formula

do you know it? the square root OF x two-x one squared plus y two - y one squared.

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the Standard form of the equation of a circle

(x-h)squared + (y-k)squared=r squared

Center of a circle

(h,k)

Unit Circle

A cirlce with radius 1 and center (0,0)

x^{2} + y^{2} =1

If x^{2} + y^{2 }=0

the radius is zero, so the "cirlce" is just a point- there really is no circle.

If you have the normal circle equation

(x+1)^{2} + (y+2)^{2} = 9, then 9 is R^{2} so the RADIUS IS 3! (not 9!)

Also, the center point, (h,k) is -1,-2

to get the GENERAL FORM of the circle equation

-you multiply out all the (x-h)^{2} and the (y-k)^{2}

-you get the general form. which is :

x^{2} + y^{2} +ax+by+c=0

If an equation is given in GENERAL FORM:

1. you MUST put it in standard form.

2. to do this, you must COMPLETE THE SQUARE!

3. Then you can find the different parts of the equation- such as the center of the circle, and the radius.

Completing the square:

Remember to add the whatever you are adding to one side to the other side too. ALSO, subtract the "c" term before doing any completing of the square.

In GENERAL FORM:

1. Everything is one one side so it equals ZERO!

2. Also, if you write something in general form do not replace the x and y with their values. Leave them as "x and y" and instead replace the center (h,k) and the radius.

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Circumscribed

A circle is around another shape

Inscribed

A circle is INSIDE another shape.

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