Pre Calculus

Question

Find an equation for the parabola described by its vertex, directrix, and focus point: vertex (√2,-√3); directrix x=2√2; focus (0,-√3)

Answer 1

The standard form of a parabola with horizontal axis is (y - k)² = 4p(x - h). You know the axis is horizontal because the directrix is vertical.

 

(h,k) are the coordinates of the vertex. So, h = √2 and k = -√3.

 

p is the (directed) distance from the vertex to the focus. Since the focus is to the LEFT of the vertex, p = -√2.

 

After you plug in the values for h, k, and p into the standard form above, you should get the answer after simplifying.

 

Please post a reply if you still have any questions or problems with this. (Hint: the parabola open to the left. You can see this if you plot the given information on a set of axes.)