Back to Derive conic equations — Problem 4 · Task Set 32

Exercises: Derive Equations of Ellipses and Hyperbolas

Show your work for each problem. Assume every conic is centered at the origin unless the problem says otherwise.

Grade 10·21 problems·~35 min·Common Core Math - HS Geometry·standard·hsg-gpe-a-3

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Fluency Practice

$Coordinate plane showing a hyperbola with two branches opening left and right from (8, 0) and (-8, 0), with a dashed central rectangle and two dashed diagonal lines through the origin$

What are the equations of the asymptotes of the hyperbola $\frac{x^2}{64} - \frac{y^2}{36} = 1$ ?

$x = 0$ and $y = 0$

$y = \frac{3}{4}x$ and $y = -\frac{3}{4}x$

$y = \frac{4}{3}x$ and $y = -\frac{4}{3}x$

$x = 8$ and $x = -8$