SOLUTION: For each of the following quadratic equations in x and y, determine which conic section it is. Acceptable answers are: ellipse, hyperbola or parabola. 86751x^2−206064xy+26649y

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: For each of the following quadratic equations in x and y, determine which conic section it is. Acceptable answers are: ellipse, hyperbola or parabola. 86751x^2−206064xy+26649y      Log On


   

Question 1161086: For each of the following quadratic equations in
x and y, determine which conic section it is. Acceptable answers
are: ellipse, hyperbola or parabola.
86751x^2−206064xy+26649y^2+826200x−1632150y+4961250= 0
Answer:
6620377x^2−541728xy+5871748y^2+103601480x+15085640y−712427600=0
Answer:
6100537x^2−3751968xy+915588y^2+37341510x−15331320y+7700625=0
Answer:
1025425x^2+342720xy+617449y^2−11596670x+6408192y+35166384=0
Answer:
75888x^2+96768xy−75888y^2−1663200x+1202400y+10080000=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

I'll do the first problem to get you started.

From this page
https://en.wikipedia.org/wiki/Conic_section#Discriminant
we see that

where Ax^2+Bxy+Cy^2+Dx+Ey+F = 0 is the general form of a conic section.

Looking at
86751x^2−206064xy+26649y^2+826200x−1632150y+4961250= 0
the coefficients are
A = 86751
B = −206064
C = 26649
D = 826200
E = −1632150
F = 4961250

We only need to worry about A,B,C for the discriminant equation. Since D is already taken in the list of coefficients, I'll use the greek letter delta for the discriminant

delta = discriminant
delta = B^2 - 4A*C
delta = (−206064)^2 - 4(86751)*(26649)
delta = 33,215,062,500

Because the result is positive, this means we have a hyperbola (according to the rules posted above).

The other problems will be solved in a similar manner. Let me know if you have any questions. Thank you.