SOLUTION: Solve the system of hyperbola 4x^2-26y^2+10=0 i spent many hour but I can't solve,the number is decimal? Thank you for help

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Solve the system of hyperbola 4x^2-26y^2+10=0 i spent many hour but I can't solve,the number is decimal? Thank you for help       Log On


   

Question 468601: Solve the system of hyperbola
4x^2-26y^2+10=0
i spent many hour but I can't solve,the number is decimal?
Thank you for help
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2-26y%5E2%2B10=0

2x%5E2-13y%5E2%2B5=0

2x%5E2-13y%5E2=-5

%282x%5E2%29%2F%28-5%29-%2813y%5E2%29%2F%28-5%29=%28-5%29%2F%28-5%29

-2x%5E2%2F5%2B%2813y%5E2%29%2F5=1

%2813y%5E2%29%2F5-2x%5E2%2F5=1

Here is the trick you probably did not think of.  You
can divide a numerator and a denominator by the same
number without changing the value:




Then cancel:




y%5E2%2F%285%2F13%29-x%5E2%2F%285%2F2%29=1


It is now in standard form 

y%5E2%2Fa%5E2+-+x%5E2%2Fb%5E2=1

a%5E2=5%2F13,  b%5E2=5%2F2

a+=+sqrt%285%2F13%29+=+sqrt%2865%29%2F13, b=sqrt%285%2F2%29=sqrt%2810%29%2F2

Since the y-term comes first, it opens upward and downward,
so a goes upward and downward

a is approximately .6 and b is approximately 1.6, draw the
defining rectangle with these corner points: 

(b,a), (b,-a), (-b,a), (-b,-a)




Then draw and extend the diagonals of the rectangle, which
will be the asymptotes of the hyperbola:




Then sketch in the hyperbola:


Edwin