Find the equation of the diameter of hyperbola 16x2 - 9y2 = 144, which is conjugate to the diameter whose equation is x = 2y.
32y = 9x
32x = 9y
16y = 3x
16x = 3y
Diameter of Hyperbola and Director Cirlce of Hyperbola -
Diameter of Hyperbola:
The locus of the mid-points of a system of parallel chords of a hyperbola is called a diameter of the hyperbola.
Let R (h, k) be the mid-point of the chord y = mx + c of the hyperbola.
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Let the equation of the diameter, which is conjugate to x = 2y is y = m1x
As we know that two diameters y = m1x and y = m2x are conjugates, if
Hence, the equation of the conjugate diameters is
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