Chapter 10 Section 4

Hyperbolas 

by Allison H.

               Standard form: (x-h)2  -(y-k)2 =1     or      (y-k)2- (x-h)2 =1
                                         a2             b2     a2           b2

In the formula the h term is or the x coordinate and the k term is for the y coordinate.

- if the x term is first then the hyperbola will be horizontal, if the y term is first then the hyperbola will be vertical

In the picture to the left is a hyperbola. The red dot in the middle is the center. The blue lines are the branches or the actual hyperbola, the fuchsia dots are the foci. The gray box is from the the vertices so you can se where the hyperbola are supposed to touch. The yellow lines are the asymptotes. The black lines are the axis.  

problem/story:

Once upon a time in a tenth grade English class a teacher, Mrs. Holland, was asking the class about hyperboles. From the back corner of the room little Johnny who never answered a question correct the whole year, shouted, "I KNOW THE ANSWER!" Johnny continued to give the definition, not of a hyperbole, but of the conic shape, the hyperbola. Since he had just come from math class the topic was still fresh in his mind. Mrs. Holland seeing how excited Johnny was about understanding hyperbolas, set up a problem for him to solve. She told Johnny her hyperbola was horizontal. She then told Johnny the center was going to be the origin. Mrs. Holland asked Johnny to write the equation in standard from, Johnny interrupted and argued he sill needed information, so finally Mrs. Holland told Johnny the asymptotes equation was y=+1/3x Can you help Johnny by putting the equation in standard form?

      

ANSWER:

ok, first make a list of what you know - 1) the hyperbola is horizontal 2) the center is the origin 3) the asymptotes equation is y= +1/3x

Now since the hyperbola is horizontal you know the first term is going to be the x term. then you know since the center is the origin the h and k are both going to be zero. The hardest part is going to be getting the a's and b's from the asymptotes equation. Well first you need to know the asymptotes equation is (y-k)=+b/a (x-h) Well we can look at the equation from the problem  and the 1 from the 1/3 is the B so b=1 and the 3 from the 1/3 is the A term so a=3.

Now go up to the an plug in the answers  (x-0)2 / (3)2  - (y-0)2 / (1)2 

the final answer you should get is: x2/9 - y2/1 =1 
Now the last part is graphing first step is to graph the center. The you move from the vertices the a distance or the b distance from your term depending on which on you're using first. Now from the vertices draw a box connecting the vertices. Now draw the branches or the actual hyperbola. The branches "kiss" at the x vertices. The last part is drawing the asymptotes. All you have to do is draw diagonal lines through

 

QUOTE: "Go confidently in the direction of you dreams. Live the life you have imagined." - Thoreau

What it means: It talks about being courageous and bold and to do what it is you want to do for the rest of your life. It tells you to persevere and be responsible enough for your own choices.

For more math help with hyperbolas go to:

http://occawlonline.pearsoned.com/bookbind/pubbooks/demana_awl/chapter1/medialib/studytips/chapter8.html

For more quotes go to: www.quotationspage.com

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