The equation of a conic section is 2y2 – x – 8y + 5 = 0. what is the equation in graphing form?

If you mean solve for y to input into calculator
2y^2-x-8y+5=0
2y^2-8y=x-5
complete the square with y
2(y^2-4y)=x-5
2(y^2-4y+4-4)=x-5
2((y-2)^2-4)=x-5
2(y-2)^2-8=x-5
2(y-1)^2=x+3
(y-1)^2=(x+3)/2
y-1=√((x+3)/2)
y=1+√((x+3)/2)

or we can graph it by hand
(y-1)^2=(1/2)(x+3)
it is a horizontal hyperbola
get into (y-k)^2=4P(x-h) form
(y-1)^2=4(1/8)(x-(-3))
since P>0, graph opens to right
P is distance from directix to vertex and from vertex to focus

vertex is (-3,1)
directix is x=-3.125
focus is (-2.875,1)
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