Question

How do you find the focus, vertex, and directrix of `x^2+10x+4y+33=0`?

Answer 1

Vertex = ( -5, -2 )
Focus = ( -5 , -3 )
Directrix = y = - 1
p = 1

Explanation:

Complete the square for 'x'
Put in form # (y −h)= 1/ (4 p)(x−k)^2#
Then (h,k) is the vertex location and p= distance from
the vertex to the directrix and focus