CON005 · Conic sections · Classes 11–12
Parabola standard equations
A parabola with vertex at the origin has one of four standard forms, opening right, left, up or down. In each, the focus is a units from the vertex and the latus rectum is 4a.
y² = 4axParabola standard equations
📐 Formula
y² = ±4ax, x² = ±4ay
✏️ Worked example
a = 2, opening right: y² = 8x, focus (2, 0), latus rectum 8.
🌍 Where it is used
Designing reflectors and bridges.
❓ Quick check
Which parabola opens downwards?
🏋️ Practice
EasyFocus of y² = 12x?
Answer: (3, 0)
MediumLatus rectum of x² = 20y?
Answer: 20
ChallengeWhich way does y² = −6x open?
Answer: Left