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Concept · Geometry & Algebra
Conic sections
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A Geometry & Algebra set, untimed
Named traps
8 ways this goes wrong.
Each is a named misconception the questions are built to catch. Open one for the move that tempts, and the fix.
- Asymptote a/b swappedSwaps a and b in the hyperbola asymptote slope b/a.→
- Ellipse focal-sum forgottenForgets |PF1|+|PF2|=2a in ellipse problems.→
- Focal-to-directrix conversion missedFails to convert a focal distance to a directrix distance when minimizing a weighted sum.→
- Focal-triangle area shortcut misusedMisapplies the focal-triangle area (tan(θ/2) / Pythagorean with 2c) relation.→
- Midpoint-chord sign errorUses the wrong sign in the point-difference (midpoint) relation, esp. hyperbola vs ellipse.→
- Parabola focal-offset errorUses the wrong p/2, or adds instead of subtracts, converting focal distance to an x-coordinate.→
- Wrong eccentricity relationApplies the ellipse eccentricity relation to a hyperbola (or keeps an e≤1 root where e>1 is required).→
- a-b-c relation confusedMixes the ellipse a2=b2+c2 with the hyperbola c2=a2+b2.→
Key formulas
No formula sheet is matched to this concept yet. Work it from first principles, and watch the traps.
The full mathematics formula sheet→Shaky underneath?
If the concept underneath still feels loose, patch it here before coming back to CSCA questions.
FoundationsPrecalculus bridgeAlgebra 2 foundations