Question

Question #d5863

Answer 1

The equation of parabola is `y=-1/16(x-3)^2-6`

Explanation:

Focus is at `(3,-10)`and directrix is `y=-2`. Vertex is at midway

between focus and directrix. Therefore vertex is at `(3,(-10-2)/2)`

or at `(3, -6)` . The vertex form of equation of parabola is

`y=a(x-h)^2+k ; (h.k) ;` being vertex. `h=3 and k = -6`

So the equation of parabola is `y=a(x-3)^2-6`. Distance of

vertex from directrix is `d= 6-2=4`, we know `d = 1/(4|a|)`

`:. 4 = 1/(4|a|) or |a|= 1/(4*4)=1/16`. Here the directrix is above

the vertex , so parabola opens downward and `a` is negative.

`:. a= -1/16` . The equation of parabola is `y=-1/16(x-3)^2-6`

graph{-1/16(x-3)^2-6 [-71.1, 71.14, -35.56, 35.56]} [Ans]