SOLUTION: Write the standard equation and define type of conic section 16x^2-196x+288-9y^2=0

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write the standard equation and define type of conic section 16x^2-196x+288-9y^2=0      Log On


   

Question 866623: Write the standard equation and define type of conic section
16x^2-196x+288-9y^2=0
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
16x%5E2-196x%2B288-9y%5E2=0
-
-
16x%5E2-196x-9y%5E2=-288
16%28x%5E2-%2849%2F4%29x%29-9y%5E2=-288----This should be a hyperbola...
16%28x%5E2-%2849%2F4%29x%2B%2849%2F8%29%5E2%29-9y%5E2=-288%2B16%2849%2F8%29%5E2---Completing the Square
16%28x-49%2F8%29%5E2-9y%5E2=-288%2B%284%2A4%2A7%2A7%2A7%2A7%29%2F%282%2A4%2A2%2A4%29
16%28x-49%2F8%29%5E2-9y%5E2=-288%2B49%2A49%2F4=%282401%2F4-288%29
16%28x-49%2F8%29%5E2-9y%5E2=%282401-1152%29%2F4
16%28x-49%2F8%29%5E2-9y%5E2=1249%2F4
%284%2F1249%2916%28x-49%2F8%29%5E2-%284%2F1249%299y%5E2=1
%2864%2F1249%29%28x-49%2F8%29%5E2-%2836%2F1249%29y%5E2=1
highlight%28%28x-49%2F8%29%5E2%2F%281249%2F64%29-y%5E2%2F%281249%2F36%29=1%29
-
Note that a%5E2=1249%2F64 and b%5E2=1249%2F36.