SOLUTION: the focus of a parabola is (5,5) and directrix is y= -3 . write an equation for the parabola and then draw the graph.

Question 552789: the focus of a parabola is (5,5) and directrix is y= -3 .
write an equation for the parabola and then draw the graph.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
the focus of a parabola is (5,5) and directrix is y= -3 .
write an equation for the parabola and then draw the graph.
**
Given position of directrix shows this is a parabola which opens upwards.
Its standard form: (x-h)^2=4p(y-k), with (h,k) being the (x,y) coordinates of the vertex.
Axis of symmetry: x=5
p=half the distance between focus and directrix on the axis of symmetry=8/2=4
y-coordinate of vertex= midpoint between focus and directrix on the axis of symmetry=(5-3)/2=1
vertex: (5,1)
Equation:
(x-5)^2=16(y-1)
or
y=(1/16)(x-5)^2+1
see graph below:

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