Avery has a job where she has a take home salary each month of 1200. If Avery wants to spend no more then 25% of her monthly tak
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If the center is at (0, 0) and the vertex is at (20, 0), then the distance, a, is the length from the center to the vertex, 20. The distance from the center to the focus is c. The distance from the center to the focus is 16, so c = 16. The formula we use to find the focus is 
. We have our c value and our a value, so we will sub in those to find b. 
and 256 = 400 - b^2. -b^2 = -144, so b = 12. There you go!
By definition, we have
So, we have to solve two different equations, depending of the possible range for the variable. We have to remember about these ranges when we decide to accept or discard the solutions:
Suppose that
In this case, the absolute value doesn't do anything: the equation is
We are supposing , so we can accept this solution.
Now, suppose that . Now the sign of the expression is flipped by the absolute value, and the equation becomes
Again, the solution is coherent with the assumption, so we can accept this value as well.