Length of the latus rectum of the hyperbola `xy-3x-4y+8=0`

1.	Length of the latus rectum of the hyperbola `xy-3x-4y+8=0`
Answer» Equation of given hyperbola is, `xy-3x-4y+8 = 0` `=>x(y-3)-4(y-3)-12+8 = 0` `=>(x-4)(y-3) = 2^2` So, this is a standard form of rectangular hyperbola, `XY = a^2/2`. `:. a^2/2 = 2^2 = 4 => a^2 = 8=> a = 2sqrt2` Length of latus rectum of rectangular hyperbola `= 2a = 2**2sqrt2 = 4sqrt2`

Discussion

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