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Selected answers to common questions:
Direct and indirect variation.
Slope, slope-intercept, standard form.
- Line Crossing Horizontal and Vertical Asymptotes [03/16/1999]
For the function y = (5x+1)/(x^2-1), why does the line between its two
vertical asymptotes and one horizontal asymptote cross?
- Line Dividing a Plane [05/11/2001]
Given a square (graphed on the Cartesian coordinate system) and a point
in the square, draw a line through the point that will divide the square
into two regions: one the smallest area possible, the other the largest
- Line of Best Fit [8/1/1996]
Are a best-fit line, a line of best fit, and a fitted line synonymous?
- Lines and t-tables [11/09/1996]
How do you use t-tables to graph lines?
- Lines Partitioning a Plane [03/09/1998]
Into how many disjoint regions do n coplanar lines partition the plane?
- Lines Tangent to a Hyperbola [07/14/1998]
If y = 2x + k is a line tangent to the graph x^2 + y^2 = 1, what is k?
- Locus of the Midpoint of a Chord [03/13/1998]
Show that the locus of the midpoint of the chord is a hyperbola.
- Manipulating Roots [08/08/1998]
If a and b are the roots of the equation 3x^2 - 5x + 1 = 0, find the
equation whose roots are a/b and b/a.
- Mapping 3D Line Segments [10/06/1997]
How do I map 3D line segments onto a 2D perspective as seen from an
arbitrary point in space?
- Minimum Distance [02/07/1998]
What is the minimum possible distance between a point on the graph of
x^2+y^2 = 1 and a point on the graph of xy = 1?
- More Questions on Finding the Equation of a Circle [10/1/1995]
Find the equation of the circle containing the points (-1, -2) and (6,-1)
and touching the x-axis.
- Moving a Circle on a Polar Graph [05/04/2001]
How do you move a circle so the center is not (0,0), but to where the
center can be (r,[theta])?
- Multiplying or Dividing by a Negative Number [04/08/1999]
When x(x-4) is less than 0...
- Naming and Graphing Functions [06/16/1997]
Can you tell me about the different families of functions?
- Non-parallel Glide Reflections [10/21/1998]
A glide reflection consists of a line reflection and a translation
parallel to the reflection. What if the translation is not parallel to
- Oblique Asymptote [4/13/1996]
I have a question about the oblique asymptote of the function: F( X
) = ( X^3 - 3X^2 + 2X - 8 ) / ( X^2 + 4X + 4
- Oblique Asymptotes [04/03/2002]
I'm stuck on how to calculate oblique limits, for example, x^2/(x-3).
- Order of Quadrant Numbers [10/21/2002]
Why are quadrants numbered that way?
- Parabola [12/23/1997]
Find the vertex, axis of symmetry, directrix, focus, distance from the
vertex to the focus, and the latus rectum.
- Parabola Equation [5/15/1995]
I'm trying to learn equations of parabolas. The example given is: find
the equation of the parabola with vertex (0,0) and focus (0,-3)...
- Parabola Equations [05/12/1997]
Deriving the standard equation for a parabola from its focus and
directrix; manipulating this equation to change the graph's appearance.
- Parabola Focal Point [7/3/1996]
What are the rules for the focal point of a parabola?
- Parabola Problems [2/23/1997]
A culvert is shaped like a parabola, 18 centimeters across the top and 12
centimeters deep. How wide is the culvert 8 centimeters from the top?
- Parabolas Through Pairs of Points [07/13/2002]
Can infinitely many parabolas pass through any two points in a plane?
- Parabola with Horizontal or Vertical Axis [05/03/2001]
How can I find the focus and directrix of a parabola whose axis is either
horizontal or vertical, like 2x^2 = -y?
- Parabolic Equation of an Arch [05/25/1998]
Finding the equation of the parabola in the McDonald's golden arches.
- Parametric Equations [07/21/1998]
A curve is given parametrically by the equations: x = (3-2k)^2 and y
= (2+k)^2. Find dy/dx, the x-intercept, the cartesian equation...
- Perpendicular Distance [04/10/1998]
Prove that the distance from a line ax + by + c = 0 to the point (h,k) is
(a*h + b*k + c)/(a^2+b^2)^(1/2).
- Piecewise Function [10/23/2001]
How do you graph the piecewise function?
- Piecewise Functions on TI Graphing Calculators [02/08/2005]
I was wondering if you could tell me how to graph a piecewise function
on a TI-83 plus graphing calculator?
- Piecewise Notation and Absolute Value [9/9/1996]
How do I use piecewise notation to write x in terms of y for "y=2x+
- Point Contained by a Circle [8/8/1995]
How can I tell if an arbitrary point on a plane is contained by a circle?
- Point inside a Triangle [07/15/2001]
Given four points, three of them the corners of a triangle, is there a
formula to determine whether or not the fourth is inside the triangle?
- Point Inside or Outside Triangle? [08/02/2001]
I have coordinates of three vertices of the triangle and coordinates of
- Point on a Line [03/23/2001]
Can you please tell me a formula to find if a point exists on a line?
Both are in x,y form.
- Points Equidistant from Point and Line [08/30/2001]
I have to plot as many points equidistant from a point and a line as
possible, and join them to get the locus.
- Points Where a Parametric Equation Crosses Itself [10/12/2001]
Find all the points where the function of the parametric equation: x=
t(9-t^2) and y=(t^2-1)(t^2-9) crosses itself...
- Polar Coordinates and Logarithmic Spirals [04/25/2004]
The polar coordinate graph of a logarithmic spiral suggests that for a
given angle, there is more than one possible r-value, since the graph
continues to spiral around itself. How is it possible for an
angle to be associated with more than one r?
- Polar Coordinates From Cartesian Coordinates [07/27/1998]
How do you find the polar coordinates from the Cartesian coordinate (3, -
- Polar Equation of a Circle [4/12/1997]
Given the polar equations r = a*sin (theta) and r = a*cos (theta), what
influence does a have on the graph?