Hyperbola

We have
Angle between assymptotes is given by

The general equation of a hyperbola with horizontal transverse axis is: where is the distance between the foci, and is the eccentricity. We know the relationship: Also, for a hyperbola, . Step 1: Use given data From the problem, we are given that the distance between the foci is 16, so , implying that: Also, the eccentricity , so: Step 2: Calculate Using the relationship , we can solve for : Step 3: Write the equation Substitute the values of and into the standard equation of the hyperbola: Multiplying both sides by 32 gives: Thus, the equation of the hyperbola is .