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MDE has the ability to classify and generate text descriptions for equations in two variables such as conic sections. MDE sonification and graphing components may be able to handle some equations for which descriptions are not yet available. Table 2.1 shows some equation types and examples that MDE supports.
Example Equations
Equation Type
Cartesian Form Example(s)
Polar Form Example(s)
NULL SET
x-c=x
r-2=r
SINGLE POINT
x^2+y^2=0,
x^2+(3-y)^2=0
r=0
ALL POINTS
x=x
r=r
VERTICAL LINE
x=c
r=1/cos(theta)
HORIZONTAL LINE
y=c
r=1/sin(theta)
TWO PARALLEL LINES
x^2=c,
y^2=c,
(x-y)^2=c
TWO INTERSECTING LINES
x^2-(x-y)^2=0
SLOPING LINE
y=3*x+4,
y=mx+b
PARABOLA
y=x^2,
y=(ay-x)^2
r=-2a/(1+cos(theta))
HYPERBOLA
x^2 - y^2 = 0
r=1/(2-2*cos(theta)+sin(theta))
ELLIPSE
x*y=1
x^2/a^2 - y^2/b^2 = 1
CIRCLE
x^2 + a*y^2 = 25
x^2 + y^2 = 25
r=5
POLYNOMIALS
y=x^3, y=3x^5
ABSOLUTE VALUE
y=abs(x)
LOGARITHM
y=log(x)
TRIG FUNCTIONS
y=sin(x)
POLAR ROSE
r = sin (a*theta)
r= cos(a*theta)
Technically, the equation solver should handle any equation of the form F1(y) = F2(y) where F1 and F2 are rational functions of the independent variable whose coefficients can be any legal expression in the independent variable.
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