Exercise 11 Page 85

We want to write the equation of a parabola with vertex (0,0) and directrix x=2. Because the directrix is the function of x, and the y-coordinate for the vertex is 0, the axis of symmetry of the parabola is the horizontal line y=0. Equation:& x=1/4 p(y- k)^2+ h Vertex:& ( h, k) Directrix:& x= h- p Since the vertex is ( 0, 0), we have that h= 0 and k= 0. Furthermore, we know that the directrix is x=2. 2 = h- p Let's substitute 0 for h in the above equation, and solve for p.

We can now write the equation of the parabola. x=1/4( - 2)(y- 0)^2+ 0 ⇔ x=-1/8y^2