, then the definition of the hyperbola gives (3) Rearranging and completing the square gives (4) and dividing both sides by results in (5) By analogy with the definition of the ellipse, define (6) so the equation for a hyperbola with semimajor axis parallel to the x-axis and s...
, then the definition of the hyperbola gives (3) Rearranging and completing the square gives (4) and dividing both sides by results in (5) By analogy with the definition of theellipse, define (6) so the equation for a hyperbola withsemimajor axis parallel to thex-axisandsemiminor axis pa...
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and intersecting the asymptotes at points and , then is constant, and (right figure above; Wells 1991). Let the point on the hyperbola have Cartesian coordinates , then the definition of the hyperbola gives (3) Rearranging and completing the square gives ...
Rearranging and completing the square gives (4) and dividing both sides by results in (5) By analogy with the definition of theellipse, define (6) so the equation for a hyperbola withsemimajor axis parallel to thex-axisandsemiminor axis ...