﻿ Find the coordinates of the foci and the equation of the directrices of the rectangular hyperbola xy = c2. : Kaysons Education

# Find The Coordinates Of The Foci And The Equation Of The Directrices Of The Rectangular Hyperbola xy = c2.

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## Question

### Solution

Correct option is

Reference to transverse and conjugate axes, as coordinate axes, the equation of hyperbola is

If e be the eccentricity, then

∴ Coordinates of foci are

Also its direction are

Now rotating the coordinate axes through an angle –π/4, the equation of hyperbola reduces to xy = c2 where c2 = a2/2, by putting  for x and y.

∴ For foci, we get

Also the equations of the directrices reduce to

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