Question 1161086
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I'll do the first problem to get you started.


From this page
<a href = "https://en.wikipedia.org/wiki/Conic_section#Discriminant">https://en.wikipedia.org/wiki/Conic_section#Discriminant</a>
we see that
<img width = "50%" src = "https://i.imgur.com/K0Ij0Lm.png">
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 <font color=red size=4>we have a <u>hyperbola</u></font> (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.
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