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Tuesday, August 7, 2012

Q.410. Equation of hyperbola given vertices and foci.

Question 410.
Write the equation of a hyperbola with vertices at (1,1) and (9, 1)
and foci at (0, 1) and (10, 1).

Answer 410.
Midpoint of vertices or foci = (5, 1) which is the center of the hyperbola
Shifting origin to (5, 1),
vertices = (-4, 0) and (4, 0) and
foci = (-5, 0) and (5, 0)
=> a = 4 and ae = 5
b^2 = a^2 (e^2 - 1) = 25 - 16 = 9
=> eqn. of the hyperbola with the new origin is
x^2/16 - y^2/9 = 1
=> equation of the hyperbola with the given vertices and foci is
(x-5)^2/16 - (y-1)^2/9 = 1.

Link to YA!

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