Step-by-Step Problem Solving
Let's tackle x² = 8y using a foolproof method that works every single time. First, identify your parabola type by matching it to the standard forms you learned.
Since x² = 8y matches x² = 4cy, you know it opens upward. Now find c by setting 4c = 8, which gives you c = 2. This value unlocks everything else!
Your focus sits at (0, c) = (0, 2), and the directrix is the line y = -c = y = -2. For the latus rectum endpoints, plug into the formulas: E₁ = (2c, c) = (4, 2) and E₂ = −2c,c = (-4, 2).
Success Strategy: Always start by identifying the parabola type - this one step makes the rest automatic!