How would you find the horizontal and vertical asymptotes of a (rectangular) hyperbola just by looking at the graph?
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a rectangular hyperbola has the property that a = b....so is you draw the axis of symmetry
then 2a = length between the vertices....at each of the vertices you draw a line segment
of length 2a perpendicular to the axis of symmetry { a units up and a units down}...
the asymptotes join the opposite endpoints { low left to high right }
then 2a = length between the vertices....at each of the vertices you draw a line segment
of length 2a perpendicular to the axis of symmetry { a units up and a units down}...
the asymptotes join the opposite endpoints { low left to high right }
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Beginning with the hyperbola alone, the asymptotes con be constructed with compass and straightedge.
Draw a line intersecting the curve in two points.
Construct a second line, parallel to the first, and also intersecting the curve in two points.
The two lines above form two chords. Construct the midpoints of the two chords, and join them with a line. This line is a diameter.
Repeat the procedure above to construct a second diameter. The two diameters intersect at the center of the hyperbola.
Draw a circle centered on the hyperbola's center and intersecting the curve in four points. These four points are vertices of a rectangle.
Construct the two lines joining the midpoints of opposite sides of the rectangle. These are the axes of the hyperbola.
It was given that the hyperbola is rectangular. Construct the two bisectors of the angle of intersection of the two axes. These bisectors are the asymptotes. Note that this last step can apply only in the case of a rectangular hyperbola.
Draw a line intersecting the curve in two points.
Construct a second line, parallel to the first, and also intersecting the curve in two points.
The two lines above form two chords. Construct the midpoints of the two chords, and join them with a line. This line is a diameter.
Repeat the procedure above to construct a second diameter. The two diameters intersect at the center of the hyperbola.
Draw a circle centered on the hyperbola's center and intersecting the curve in four points. These four points are vertices of a rectangle.
Construct the two lines joining the midpoints of opposite sides of the rectangle. These are the axes of the hyperbola.
It was given that the hyperbola is rectangular. Construct the two bisectors of the angle of intersection of the two axes. These bisectors are the asymptotes. Note that this last step can apply only in the case of a rectangular hyperbola.
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omg really? an asymtope is where the line cant pass or the line gets infinitely closer to that point but never touches it. just look for those points...