Rectangular Hyperbolas (VCE SSCE Mathematical Methods): Flashcards

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Rectangular hyperbolas
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Basic equation of rectangular hyperbola

y=1xy = \frac{1}{x} or y=x1y = x^{-1} for x0x \neq 0

Value of xx where y=1xy = \frac{1}{x} is undefined

x=0x = 0

Definition of asymptotes

Lines that curve approaches but never touches

Horizontal asymptote of y=1xy = \frac{1}{x}

y=0y = 0

Vertical asymptote of y=1xy = \frac{1}{x}

x=0x = 0

Quadrants where y=1xy = \frac{1}{x} branches lie

First and third quadrants

General form of rectangular hyperbola

y=axh+ky = \frac{a}{x - h} + k

Role of hh in y=axh+ky = \frac{a}{x - h} + k

Horizontal shift

Role of kk in y=axh+ky = \frac{a}{x - h} + k

Vertical shift

Effect of negative aa in y=axy = \frac{a}{x}

Reflection in the xx-axis

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