Prove the following theorem of Apollonius of Perga (the Greek mathematician born in 262 bce who gavethe parabola, ellipse, and hyperbola their names): The subtangent of the parabola y = x2 at x = a is equal to a/2.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 45E
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Prove the following theorem of Apollonius of Perga (the Greek mathematician born in 262 bce who gavethe parabola, ellipse, and hyperbola their names): The subtangent of the parabola y = x2 at x = a is equal to a/2.

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