Question 552780
the focus and directrix of a parabola are given. the focua is (3,5) and the directrix is y=1 . write the equation of the parabola and then draw the graph.
Standard form of equation for parabola: (x-h)^2=4p(y-k), (h,k) being the (x,y) coordinates of the vertex.
For given equation:
Parabola opens upwards
axis of symmetry: x=3
p=half the distance between directrix and focus on the axis of symmetry=4/2=2
y-coordinate of vertex=3
vertex: (3,3)
Equation of parabola:
(x-3)^2=8(y-3)
or
y=(1/8)(x-3)^2+3
{{{ graph( 300, 300, -10, 10, -10, 10,(x-3)^2/8+3) }}}