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For a hyperbola in standard form: x² a² 6² = = 1, a, b>0 the constant a is called the semifocal axis and b is the semiconjugate axis. Show that the distances of a point P(x, y) on the hyperbola from the two foci (±c, 0) are x Fa| and hence show that the absolute value of their difference is constant.

For a hyperbola in standard form: x² a² 6² = = 1, a, b>0 the constant a is called the semifocal axis and b is the semiconjugate axis. Show that the distances of a point P(x, y) on the hyperbola from the two foci (±c, 0) are x Fa| and hence show that the absolute value of their difference is constant.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For a hyperbola in standard form: x² a² 6² = 1, a, b>0 the constant a is called the semifocal axis and b is the semiconjugate axis. Show that the distances of a point P(x, y) on the hyperbola from the two foci (±c, 0) are xa| and hence show that the absolute value of their difference is constant.
Transcribed Image Text:For a hyperbola in standard form: x² a² 6² = 1, a, b>0 the constant a is called the semifocal axis and b is the semiconjugate axis. Show that the distances of a point P(x, y) on the hyperbola from the two foci (±c, 0) are xa| and hence show that the absolute value of their difference is constant.
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