If a hyperbola passing through the origin has `3x-4y-1=0`
and `4x-3y-6=0`
as its asymptotes, then find the equation of its transvers and
conjugate axes.
Text Solution
AI Generated Solution
To find the equations of the transverse and conjugate axes of the hyperbola that passes through the origin and has the given asymptotes, we can follow these steps:
### Step 1: Identify the asymptotes
The equations of the asymptotes given are:
1. \(3x - 4y - 1 = 0\)
2. \(4x - 3y - 6 = 0\)
### Step 2: Rewrite the asymptotes in slope-intercept form
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A hyperbola passes through (2,3) and has asymptotes 3x-4y+5=0 and 12 x+5y-40=0 . Then, the equation of its transverse axis is (a) 77 x-21 y-265=0 (b) 21 x-77 y+265=0 (c) 21 x-77 y-265=0 (d) 21 x+77 y-265=0
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