SOLUTION: The center of a hyperbola with equation 9x2 - 25y2 - 225 = 0 is moved 5 units to the right and 2 units down. Find the equation in standard form of the hyperbola in its new posi

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The center of a hyperbola with equation 9x2 - 25y2 - 225 = 0 is moved 5 units to the right and 2 units down. Find the equation in standard form of the hyperbola in its new posi      Log On


   

Question 1188725: The center of a hyperbola with equation 9x2 - 25y2 - 225 = 0 is moved 5 units to the right and 2 units down. Find the equation in standard form of the hyperbola in its new position.
Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.
The center of a hyperbola with equation 9x2 - 25y2 - 225 = 0 is moved 5 units to the right and 2 units down.
Find the equation in standard form of the hyperbola in its new position.
~~~~~~~~~~~~~~ 

Starting from the given equation, divide its both sides by 225.


You will get then the hyperbola equation in the standard form


    x%5E2%2F5%5E2 - y%5E2%2F3%5E2 = 1.


The center of this (given) hyperbola is the origin of the coordinate system (o,o).


After described translations, the center of the new hyperola is at the point (5,-2).


THEREFORE, the standard equation of the translated hyperbola is


     %28x-5%29%5E2%2F5%5E2 - %28y-%28-2%29%29%5E2%2F3%5E2 = 1,


or, which is the same, but simpler


     %28x-5%29%5E2%2F5%5E2 - %28y%2B2%29%5E2%2F3%5E2 = 1.      ANSWER

Solved.