Show that for e > 1, the hyperbola with foci at (± ae, 0) and directrices at x = ± ae has the equation x^2/a^2 - y^2/b^2 = 1.
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Step 1
Using the distance formula, we can write the equation for the hyperbola in terms of d and a: sqrt((x+ae)^2 + y^2) - sqrt((x-ae)^2 + y^2) = 2d Simplifying this equation by squaring both sides and rearranging, we get: (x+ae)^2 + y^2 - 2sqrt((x+ae)^2 + Show more…
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