Question 1199121

vertex should be V, not F

the formula of the parabola with vertex V({{{1}}},{{{3}}}) and directrix {{{x=3}}}

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

where {{{a}}} is the distance between directrix  and vertex 

 directrix {{{x=3}}}=>one point on directrix is ({{{3}}},{{{3}}}) 

other point  is ({{{1}}},{{{3}}})


{{{a=sqrt((3-1)^2+(3-3)^2)}}}
{{{a=sqrt(4)}}}
{{{a=2}}}

{{{(y-3)^2=-4(2)(x-1)}}}

{{{(y-3)^2=-8(x-1)}}}


{{{ drawing( 600, 600, -10, 10, -10, 10,
circle(1,3,.12),locate(1,3,V(1,3)),
blue(line(3,-10,3,10)),
graph( 600, 600, -10, 10, -10, 10, 3 - 2sqrt(2)sqrt(1-x),2sqrt(2)sqrt(1 - x)+3) )}}}