Question

Find an equation of the figure described.

1) Parabola with focus (2,3) and directrix y=-1

Answer 1

We have to write the equation in the form

\[(x-h)^{2} = 4p (y-k)\] where (h,k) is the vertex and p is the distance between Vertex and Directrix. We found Vertex to be ( 2,1) and p = 2 since the directrix is below the vertex p is positive and the parabola opens up.

Now we can substitute the values in the equation and find the final answer.

\[(x-2)^{^{2}} = 4 \times 2 ( y-1)\] \[\frac{ 1 }{ 8} (x - 2 )^{2} = y - 1\]\[y = \frac{ 1 }{ 8 }(x-2)^{2} + 1 \]