ConceptGeometry & Algebra

Key formulas

Slope from two points: k = (y2 − y1)/(x2 − x1); vertical line slope undefined; slope from inclination θ: k = tan θ
Line forms: point-slope y−y1=k(x−x1); slope-intercept y=kx+b; intercept x/a+y/b=1; general Ax+By+C=0
Parallel: k1=k2 (or A1B2=A2B1); Perpendicular: k1·k2=−1 (or A1A2+B1B2=0)
Point-to-line distance: d = |Ax0+By0+C| / √A²+B²
Circle standard: (x−a)²+(y−b)²=r²; general x²+y²+Dx+Ey+F=0, center (−D/2,−E/2), r=√D²+E²−4F/2 (need D²+E²−4F>0)
Ellipse: x²/a² + y²/b² = 1 (a>b>0); a² = b² + c²; |PF1|+|PF2| = 2a; e = c/a < 1
Hyperbola: x²/a² − y²/b² = 1; c² = a² + b²; asymptotes y = ±(b/a)x; ||PF1|−|PF2|| = 2a; e = c/a > 1
Parabola: y² = 2px (focus (p/2,0), directrix x=−p/2); e = 1; distance to focus = distance to directrix
Common chord of two circles: subtract the two general equations to get the chord (radical) line

If the concept underneath still feels loose, patch it here before returning to CSCA questions.

FoundationsPrecalculus bridge Algebra 2 foundations

Parabola

definition (focus/directrix), standard forms, focal distance to x-coordinate, weighted-distance minimization via directrix

No misconceptions are logged for this concept yet, so there is nothing named here to trip you up. Practice it and anything that does catch you will be added.

Practice this concept →