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Finding the Center-Radius Form of a Circle by Completing the Square - Example 3

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Finding the Center-Radius Form of a Circle by Completing the Square - Example 3

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Conic Sections: Graphing Ellipses Part 2

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Conic Sections: Graphing Ellipses Part 2. In this video, I graph two more ellipses. The second examples requires completing the square to put it in a 'standard form'.

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Conic Sections, Hyperbola , Shifted : Find Asymptotes

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Conic Sections, Hyperbola , Shifted : Find Asymptotes. Here we find the point-slope form of the asymptotes of a hyperbola.

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Khan academy explains!

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Features of a circle from its standard equation

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Sal finds the center and the radius of the circle whose equation is (x+3)^2+(y-4)^2=49.

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Given some features of a hyperbola, find its equation.

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Center
Radius

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Center
Vertices
Endpoints
Foci

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Center
Vertices
Foci
Asymptotes
Domain
Range

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I'm going to rewrite an equation in  of a hyperbola in standard form by completing the square.
12x²-4y²-72x-16y+140=0
Move any constants to right hand side and rearrange terms leaving room to complete the square.
12x²-72x       -4y²-16y      =-140
Factor out 12 and -4
12(x²-6x)      -4(y²+4y)    =-140
Complete the square and be sure to multiply your added numbers to the factor prior to adding to the right hand side.
12(x²-6x+9)-4(y²+4y+4)=-140
+108
-16
Factor left side and simplify right side.
12(x-3)²-4(y+2)²=-48
Divide right hand side by -48 and simplify.

-(x-3)²       (y+2)²
______   + ______  =  1
4                 12
Rewrite the equation.
(y+2)2       (x-3)²
______ _ _______  =  1
12               4

Hyperbola In Standard Form

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Meagan HandleyI will solve for the radius and center of this equation:

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Meagan HandleyI will solve for the radius and center of this equation:

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10x^2-40x+10y^2+40y-40=0
divide all by 10 to get:
x^2-4x+y^2+4y-4=0
x^2-4x+y^2+4y=4
then take (-4)1/2=-2 -2^2=4
(4)1/2=2 2^2=4
(x^2-4x+4)+(y^2=4y=4)=4+4+4
Center=(2,-2)
Radius=16

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6x^2+y^2=36
Divide all by 36 so the 36 side becomes 0
(x^2/6)+(y^2)=1
Move The square root of 6 to both the left and right of origin and more the square root of 2 up and down from the origin.

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((x=36)^2/10,000)-((x-4)^2/400)=1
((x-(-36))^2/(100)^2)-((x-4)^2/(20)^2)=1
h=-36, k=4, a=100, b=20
y-4=+-(20/100)(x=36)

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You tube is know my best friend in regards to practicing math. Here is another video to help us all regarding ellipses, the not so perfect circle.
Christina Traw

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I found this video helpful when you only have the end points and have to find the radius for the circle. I am still getting mixed up when the fractions come into play. I can  deal with x and y all day just no fractions please!
Thank you
Christina Traw

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Finding the Center-Radius Form of a Circle Given the Endpoints of the Diameter

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Khan Academy is always my go to for studying walkthroughs.

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Sal introduces the standard equation for hyperbolas, and how it can be used in order to determine the direction of the hyperbola and its vertices.

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Sal introduces ellipses and shows how their standard equation relates to their center and radii (ellipses have two radii: major and minor).

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Kira I find the khan academy videos very helpful and informative. Thank you for sharing!

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Kira I find the khan academy videos very helpful and informative. Thank you for sharing!

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Christina Traw

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Ellipses!!! very cool..