Question 1119528
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The equation has a y^2 term, so the parabola opens right or left.  Vertex form for the equation of a parabola that opens right or left is<br>
{{{x-h = (1/(4p))(y-k)^2}}}<br>
where the vertex is (h,k) and p is the directed distance from the directrix to the vertex and from the vertex to the focus.<br>
Note with this form of the equation, the length of the latus rectum (perpendicular to the axis of symmetry and through the focus) is |4p|.<br>
Put the given equation in that form:<br>
{{{y^2-10x = 0}}}
{{{10x = y^2}}}
{{{x = (1/10)y^2}}}
{{{x-0 = (1/10)(y-0)^2}}}<br>
This is in vertex form.  The vertex is (0,0); p = 10/4 = 2.5.<br>
vertex: (0,0)
focus: p = 2.5 right of the vertex, at (2.5,0)
directrix: p = 2.5 left of the vertex; x = -2.5
length of latus rectum: 4p = 10