Parabolas & Circles Tutor Help
A one-page recap of center-radius and vertex forms, plus a way to ask a tutor for a worked explanation.
1 Quick recap
The essentials on one page before you ask for help.
Core forms
Circle: (x − h)² + (y − k)² = r² · center (h, k), radius r
Parabola: y = a(x − h)² + k · vertex (h, k), focus (h, k + 1/(4a)), directrix y = k − 1/(4a)
Parabola: y = a(x − h)² + k · vertex (h, k), focus (h, k + 1/(4a)), directrix y = k − 1/(4a)
x² → vertical axis; y² → horizontal axis. Complete the square to reveal hidden centers and vertices.
Stuck? Check these first
- Signs flip when reading the center: (x − 2)² means h = +2.
- The squared variable sets the axis: x² opens up/down, y² opens left/right.
- p = 1/(4a): focus is p from the vertex; directrix is p the other way.
- Circle shortcut: x² + y² + Dx + Ey + F = 0 → center (−D/2, −E/2).
2 Ask a tutor
Tell us what you are stuck on. A tutor will follow up with a worked explanation.
3 Keep going
While you wait, review the lesson or drill practice problems.