﻿ The condition for two diameters of a hyperbola  represented by Ax2 + 2Hxy + By2 = 0 to be conjugate is : Kaysons Education

# The Condition For Two Diameters Of A Hyperbola  represented By Ax2 + 2Hxy + By2 = 0 To Be Conjugate Is

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## Question

### Solution

Correct option is

Aa2 = Bb2

Let y = m1x, y = m2x be two conjugates diameters of the hyperbola

…… (1)

By assumption, diameters are represented by

Ax2 + 2Hxy + By2 = 0. Put y = mx in it

Ax2 + 2HmxBm2x= 0

⇒      Bm2 + 2Hm + A = 0                                           …. (2)

Then this equation has roots m1, m2

…. (3)

The two diameter are conjugate

⇒       Aa2 = Bb2

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