Cheatography

# Geometry I Cheat Sheet by doxeado

Formulas for the basic topics of analytical geometry.

### Line

 General equation Ax+By+C=0 Point slope equation y-y1=m­(x-x1) Slope of a straight line (m) m=-A/B m=(y2-­y1)­/(x­2-x1) m=tg(α)

### Positions relative to two lines

 Equations Ax+By+C=0A'x+B'y+C'=0 Secant lines A/A'≠B/B' Parallel lines A/A'=B/B'≠ C/C' Coincident lines A/A'=B/B'= C/C'

### Parallel lines

 Slope m1=m2 -A/B=-­­A'/B'

### Perpen­dicular lines

 Slope m1.m2=-1 -A/B=B'/A'

### Points

 Coordi­nates P(x1,y1) Q(x2,y2) M(x3,y3) Distance between two points (P and Q) d=√[(x2-x­1)^­2+(­y2-­y1)^2] Midpoint (M) x3=(x1­+x2)/2 y3=(y1­+y2)/2 Distance from a point (P) to a line d=|(A.x­1+­B.y­1+C)/√(a^2+b^2)|

### Circum­ference

 Ordinary equation (x-a)^­2+(­y-b­)^2=r^2 Elements Center: C(a,b) Point: P(x,y) Radius: r General equation x^2+y^2+Ax+By+C=0 If: (A/2)^2+(B/2)^2-C>0 x and y don't multiply x^2 and y^2 have 1 as coefficient Elements A=-2a B=-2b C=a^2+b^2-r

### Parabola

 General equation Ax^2+B­xy+­Cy^­2+D­x+E­y+F=0 If: A≠0 v B≠0 B^2-4AC=0 Vertical Parabola Ordinary Equation (x-x0)­^2=­2p(­y-y0) Vertex: V(x0,y0) Parameter: p Horizontal Parabola Ordinary Equation (y-y0)­^2=­2p(­x-x0) Vertex: V(x0,y0) Parameter: p

### Hyperbola

 General equation Ax^2+B­xy+­Cy^­2+D­x+E­y+F=0 If: A≠0 ^ B≠0 A.B<0 Ordinary Equation (horiz­ontal focal axis) [(x-x0­)^2­]/(­a^2­)-[­(y-­y0)­^2]­/(b­^2)=1 Ordinary Equation (vertical focal axis) [(y-y0­)^2­]/(­b^2­)-[­(x-­x0)­^2]­/(a­^2)=1 Equila­teral Hyperbola Equation a=b Asymptotes y=x y=-x Elements Center: O(x0,y0) Length of the semimajor axis of the hyperbola: a Length of the semi-minor axis of the hyperbola: b