Question 1168877
given: the length of latus rectum (LR) is {{{10}}} 

The length of latus rectum for a standard equation of a parabola {{{y^2 = 4px}}} is equal to {{{LR = 4p}}}

=>{{{4p=10}}}

then {{{p=10/4=5/2}}} and foci is at ({{{5/2}}},{{{0}}})

and your equation is:

{{{y^2 = 10x}}}


{{{drawing( 600, 600, -10, 10, -10, 10, 
circle(5/2,0,.12), locate(5/2,0.5,F(5/2,0)),
circle(5/2,5,.12),circle(5/2,-5,.12),blue(line(5/2,5,5/2,-5)),
 graph( 600, 600, -10, 10, -10, 10, sqrt(10x),-sqrt(10x))) }}}