Can you help me with this parabola problem?

Question

A. Write the  equation for the parabola whose focus is at (5,-1) and directrix  is at x=3

 

B. White the equation for the hyperbole for which the length of the traverse acid is 6 units and the foci are at (0,5) and (0,-5)

 

Answer 1

B:  transverse axis runs vertically, along the y-axis; c = 5 and 2a = 6 so a = 3.

 

Also, in general, c² - a² = b²  = 25 - 9 = 16; therefore b = 4.

 

Equation is y²/9 - x²/16 = 1.