Question 1001602

Write an equation of the parabola with vertex (3, 1) and focus (3, 5).

 Write an equation:
Vertex is ({{{5}}},{{{4}}})
Focus is ({{{8}}},{{{4}}}) 

The equation of a parabola with vertex ({{{h}}},{{{k}}}) is either

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

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

where the vertex is ({{{h}}},{{{k}}}),  {{{p}}} is distance from vertex to focus 

Since the vertex is ({{{5}}},{{{4}}}), {{{h = 5}}} and {{{k = 4}}}.

Since the vertex ({{{5}}},{{{4}}}) and focus ({{{8}}},{{{4}}}) have the same y-coordinate, it is equation of the second type.

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

The distance from vertex to focus is {{{3}}} units. Since the focus is right of the vertex, {{{p}}} is positive, and so {{{p = 3}}}. (Parabola opens to the right)

So the equation is

{{{(y - 4)^2 = 4*3(x - 5)}}}

{{{(y - 4)^2 = 12(x - 5)}}}


{{{(y - 4)^2/12 = x - 5}}}


{{{(1/12)(y - 4)^2+5 = x }}}

it cannot be this:
x= 1/4c y^2 (x-h)^2  + k....here is something wrong