for this problem, i've been given the vertices of the hyperbola as (4, pi/2) and (-1, 3pi/2). the question asks to find the polar equation of this hyperbola. so what i did was do a quick sketch of the graph. (4, pi/2) is essentially (0,4) and (-1, 3pi/2) is essentially (0,1). the midpoint of the two vertices is (0,2.5) so that's the center. since the focus is at (0,0), c = 2.5 and a = 1.5 therefore e = c/a and e = 5/3 so i wrote out the equation r = (5/3)p / 1 + (5/3)sin& since the directrix is above the x axis or polar axis between the two vertices. (by the way i'm using "&" to stand for the greek letter theta.) then i just used one of the points they gave me (4, pi/2) and plugged it into the equation to solve for p. 4 = (5/3)p / (1 + (5/3)) when i solve for p, i get that p = 32/5. however when i plug in the other point they gave me for the hyperbola (-1, 3pi/2), i get a different p value. -1 = (5/3)p / (1 - (5/3)) and when i solve for p i get that p = 2/5. what's going on? how come the p values are different? both points are vertices of the hyperbola so i don't know why i'm getting different answers. the back of my textbook says that p = 8/5. how did the book get that? and how am i getting two different p values? please help me! i'm so confused.