Question 606759
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Hi,
Write the conic in standard form:
y^2-10y-4x+57=0
(y^2-10y + 25) -25 -4x +57 = 0
(y-5)^2 +32 = 4x
 x = (1/4)(y-5)^2 +8
Standard Form:
 (y-5)^2 = 4(x-8)

the vertex form of a parabola opening right or left, {{{x=a(y-k)^2 +h}}} where(h,k) is the vertex.
The standard form is {{{(y -k)^2 = 4p(x -h)}}}, where  the focus is (h +p,k )
{{{drawing(300,300,   -20,20,-20,20, grid(1),
graph( 300, 300, -20,20,-20,20,0,5 + sqrt(4x -32),5 - sqrt(4x -32)  ))}}}