Advanced Math/hyperbola

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Expert: Robi Bhattacharjee - 8/9/2008


Question
i was wondering if you could please put the hyperbola      -4x^2 + 9y^2 - 32x +90y +17 = 0  in standard form

Answer
Hello John,


-4x^2 + 9y^2 - 32x + 90y + 17 = 0

-4x^2 - 32x + 9y^2 + 90y = -17

-4(x^2 + 8x) + 9(y^2 + 10y) = -17

-4(x^2 + 8x + 16) + 9(y^2 + 10y + 25) = -17 + -4*16 + 9*25

-4(x + 4)^2 + 9(y + 5)^2 = 144

9(y+5)^2 - 4(x+4)^2  
-------------------  =   1
      144

(y+5)^2     (x+4)^2
-------  +  -------   = 1
 16          36


So that is it. I used a method called completing the square. All I did was add numbers to two sides of equation, and then factor.


I am awfully sorry that no one answered your question sooner.

Feel free to ask,

Robi

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Robi Bhattacharjee

Expertise

I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

Experience

I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

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I am in the San Diego Math Circle

Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

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