Tricky Oblique Parabola Question?

[math12345]

Please help with this! I cannot seem to figure it out.

A parabola has a focus (1,1) and a vertex (4,5).
Find the equation of the directrix, the endpoints of the latus rectum, and the equation in standard form.

I have plotted the points but I have no idea how to get the equation because it is not a normal parabola. Please help!

 

[QuarkCharmer]

Find the distance between the focus and the vertex (distance formula). Then find the equation of a line that passes through both of those points. From there, you should be able to find the directrix, remember that the directrix will be of equal distance as the one from the vertex to the focus, but in the opposite direction. Once you find that point, finding a line perpendicular to the one you did before, passing through the point of the directrix should satisfy that first part.

The endpoints of the Latus Rectum are going to be two places on a line perpendicular to that central symmetry line. Once you find that line (perpendicular with that line and through the focus), you can set it equal to the parabola and solve for the end points.

As you can see, the key to solving this problem is to find the equation of the line that connects the vertex and focus first thing. Everything else works out from that by finding lines that are perpendicular.