Digital ACT Math Practice Question #831
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Recall that slope is \( \frac{\Delta y}{\Delta x} \). The \( y \)-denominator gives \( b^2 \) and the \( x \)-denominator gives \( a^2 \).
Tactical Method: Slope is always the vertical scale factor divided by the horizontal scale factor: \( \frac{\sqrt{36}}{\sqrt{25}} = \frac{6}{5} \).
For a horizontal hyperbola of the form \( \frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1 \): The slopes of the two linear asymptotes are \( m = \pm \frac{b}{a} \). From the equation: \( a^2 = 25 \implies a = 5 \) \( b^2 = 36 \implies b =...
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