Question

Question #34f03

Answer 1

The equation of parabola is `y=-1/18(x-4)^2 +1.5`

Explanation:

Focus is at `(4,-3)`and directrix is `y=6`. Vertex is at midway

between focus and directrix. Therefore vertex is at `(4,(6-3)/2)`

or at `(4, 1.5)` . The vertex form of equation of parabola is

`y=a(x-h)^2+k ; (h.k) ;` being vertex. `h=4 and k = 1.5`

So the equation of parabola is `y=a(x-4)^2 +1.5`.

Distance of vertex from directrix is `d= 6-1.5=4.5`, we know

`d = 1/(4|a|):. 4.5 = 1/(4|a|) or |a|= 1/(4.5*4)=1/18`. Here the

directrix is above the vertex , so parabola opens downward and

`a` is negative. `:. a=-1/18` . The equation of parabola is

`y=-1/18(x-4)^2 +1.5`

graph{-1/18(x-4)^2+1.5 [-20, 20, -10, 10]} [Ans]