Question 747205

given:

1) vertex (0,0)=(h,k) and focus (0,3)=(h,k+a)

standard equation: if vertex and focus have same {{{x}}} coordinate, equation is

{{{(x-h)^2=4a(y-k)}}}

so, your equation is:

{{{(x-0)^2=4a(y-0)}}}

{{{x^2=4ay}}}........since (0,3)=(h,k+a) => {{{k+a=3}}}=> {{{0+a=3}}} => {{{a=3}}}

{{{x^2=4*3y}}}

{{{x^2=12y}}}

{{{y=(1/12)x^2}}}

{{{ drawing( 600, 600, -10, 10, -10, 10,circle(0,0,0.2),circle(0,3,0.2),graph( 600, 600, -10, 10, -10, 10, (1/12)x^2)) }}}