Find the coordinates of vertex, focus, and equation of the directrix of the equation 2x^2-32x-y+127=0.

Answer 1

2x^2 -32x-y+127=0

Need to put in conic form 4p(y-k)= (x-h)^2 where p is focal distance and (h.k)is vertex

y-127= 2x^2-32x

y-127= 2(x^2-16x)

y-127 =2( x-8)^2 -128

y+1= 2(x-8)^2

(1/2) (y+1) = (x-8)^2

So vertex is at ( 8,-1)

4p=1/2 so focal length is 1/8 and focus is at ( 8,-7/8) and equation of directrix is y= - 9/8