What is the equation of the parabola with a focus at (7,3) and a directrix of y= 4?

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Answer 1 · 2017-08-15T12:10:30

The equation of parabola is #y= - 0.5 (x-7)^2+3.5#

Focus is at #(7,3)# , Directrix is # y =4# . The vertex is at midway

between focus and directrix .

So vertex is at #(7,(3+4)/2) or (7,3.5)# , The distance between

vertex and directrix is # d= 4-3.5 = 0.5 # . Here directrix is above

vertex , so parabola opens downward and #a# is negative.

#d =1/(4|a|) or 0.5 = 1/(4|a|) :. |a| = 1/2 , a = - 0.5#

The equation of parabola is #y= a(x-h)^2+k ; (h,k)#

being vertex. Here # h= 7 , k= 3.5 ,a = - 0.5 # . Hence

the equation of parabola is #y= - 0.5 (x-7)^2+3.5#

graph{-0.5(x-7)^2 +3.5 [-20, 20, -10, 10]}