←All concepts
Concept · Geometry & Algebra
Line equation forms
point-slope, slope-intercept, two-point, intercept, general Ax+By+C=0
Practice this concept→
A Geometry & Algebra set, untimed
Nothing named here yet.
No misconceptions are logged for this concept, so there is nothing named to trip you up. Practice it, and anything that does catch you will be added.
Key formulas
9- Slope from two pointsk = (y2 − y1)/(x2 − x1)vertical line slope undefinedslope from inclination θ: k = tan θ
- Line formspoint-slope y−y1=k(x−x1)slope-intercept y=kx+bintercept x/a+y/b=1general Ax+By+C=0
- Parallel: k1=k2 (or A1B2=A2B1)Perpendicular: k1·k2=−1 (or A1A2+B1B2=0)
- Point-to-line distanced = |Ax0+By0+C| / √A2+B2
- Circle standard(x−a)2+(y−b)2=r2general x2+y2+Dx+Ey+F=0, center (−D/2,−E/2), r=√D2+E2−4F/2 (need D2+E2−4F>0)
- Ellipsex2/a2 + y2/b2 = 1 (a>b>0)a2 = b2 + c2|PF1|+|PF2| = 2ae = c/a < 1
- Hyperbolax2/a2 − y2/b2 = 1c2 = a2 + b2asymptotes y = ±(b/a)x||PF1|−|PF2|| = 2ae = c/a > 1
- Parabolay2 = 2px (focus (p/2,0), directrix x=−p/2)e = 1distance to focus = distance to directrix
- Common chord of two circlessubtract the two general equations to get the chord (radical) line
Shaky underneath?
If the concept underneath still feels loose, patch it here before coming back to CSCA questions.
FoundationsPrecalculus bridgeAlgebra 2 foundations