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General equation
Ax+By+C=0
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Point slope equation
y-y1=m(x-x1)
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Slope of a straight line (m)
m=-A/B
m=(y2-y1)/(x2-x1) m=tg(α) |
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Equations
Ax+By+C=0
A'x+B'y+C'=0 |
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Secant lines
A/A'≠B/B'
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Parallel lines
A/A'=B/B'≠ C/C'
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Coincident lines
A/A'=B/B'= C/C'
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Slope
m1=m2
-A/B=-A'/B' |
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Slope
m1.m2=-1
-A/B=B'/A' |
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Coordinates
P(x1,y1)
Q(x2,y2) M(x3,y3) |
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Distance between two points (P and Q)
d=√[(x2-x1)^2+(y2-y1)^2]
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Midpoint (M)
x3=(x1+x2)/2
y3=(y1+y2)/2 |
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Distance from a point (P) to a line
d=|(A.x1+B.y1+C)/√(a^2+b^2)|
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Ordinary equation
(x-a)^2+(y-b)^2=r^2
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Elements
Center: C(a,b)
Point: P(x,y) Radius: r |
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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 |
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Elements
A=-2a
B=-2b C=a^2+b^2-r |
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Equation
[(x-x0)^2]/(a^2)+[(y-y0)^2]/(b^2)=1
Center: C(x0,y0) Horizontal radius: a Vertical radius: b |
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General equation
Ax^2+Bxy+Cy^2+Dx+Ey+F=0
If: A≠0 v B≠0 B^2-4AC=0 |
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Vertical Parabola Ordinary Equation
(x-x0)^2=2p(y-y0)
Vertex: V(x0,y0) Parameter: p |
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Horizontal Parabola Ordinary Equation
(y-y0)^2=2p(x-x0)
Vertex: V(x0,y0) Parameter: p |
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General equation
Ax^2+Bxy+Cy^2+Dx+Ey+F=0
If: A≠0 ^ B≠0 A.B<0 |
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Ordinary Equation (horizontal focal axis)
[(x-x0)^2]/(a^2)-[(y-y0)^2]/(b^2)=1
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Ordinary Equation (vertical focal axis)
[(y-y0)^2]/(b^2)-[(x-x0)^2]/(a^2)=1
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Equilateral Hyperbola Equation
a=b
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Asymptotes
y=x
y=-x |
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Elements
Center: O(x0,y0)
Length of the semimajor axis of the hyperbola: a Length of the semi-minor axis of the hyperbola: b |
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