SOLUTION: Graph the equation. Identify the conic section. Then find the domain and range. 4x^2-24y^2-144=0. Please help me solve this

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Graph the equation. Identify the conic section. Then find the domain and range. 4x^2-24y^2-144=0. Please help me solve this      Log On


   

Question 136818: Graph the equation. Identify the conic section. Then find the domain and range.
4x^2-24y^2-144=0. Please help me solve this
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's see what kind of conic section you have by algebraic manipulation of your equation:
4x%5E2-24y%5E2-144+=+0 Add 144 to both sides.
4x%5E2-24y%5E2+=+144 Now divide both sides by 144.
%284x%5E2-24y%5E2%29%2F144+=+1 Simplify this.
%28x%5E2%2F36%29-%28y%5E2%2F6%29+=+1 Compare this with the standard form of an equation of a hyperbola with center (0, 0) and vertices on the x-axis:
%28x%5E2%2Fa%5E2%29-%28y%5E2%2Fb%5E2%29+=+1
To graph this equation, you will need to solve it for y and, if done correctly, you will get a positive solution and a negative solution for y.
You can then graph these two solutions to see the hyperbola.
%28x%5E2%2F36%29-%28y%5E2%2F6%29+=+1 Solve for y:
y%5E2%2F6+=+%28x%5E2%2F36%29-1 Simplify the right side then multiply both sides by 6.
y%5E2+=+%28x%5E2-36%29%2F6 Take the square root of both sides.
y+=+sqrt%28%28x%5E2-36%29%2F6%29 and y+=+-sqrt%28%28x%5E2-36%29%2F6%29
Now graph these two equations:

The domain ( the set of all possible values of the independent variable (x)) is, as can be seen on the graph:
-6%3Ex%3E6
The range (the set of all possible values of the dependent variable (y)) is:
Y = all real numbers.