Home
Class 11
MATHS
Length of the latus rectum of the hyperb...

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

Text Solution

Verified by Experts

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`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the eccentricity, coordinates of the foci, equations of directrices and length of the latus rectum of the hyperbola 3x^2-y^2=4

The length of the latus rectum of the hyperbola 3x ^(2) -y ^(2) =4 is

The length of the latus rectum of the hyperbola 3x ^(2) -y ^(2) =4 is

The length of the latus rectum of the hyperbola x^(2) -4y^(2) =4 is

The length of the latus rectum of the hyperbola x^(2) -4y^(2) =4 is

Find the eccentricity,coordinates of the foci equations of directrices and length of the latus rectum of the hyperbola 3x^(2)-y^(2)=4

Find the centre, foci, eccentricity equation of the directrices, length of the latus rectum of the hyperbola. x^(2)-4y^(2)=4

Find the centre, foci, eccentricity equation of the directrices, length of the latus rectum of the hyperbola. x^(2)-4y^(2)=4

Find the vertex, focus, directrix and length of the latus rectum of the parabola y^2 - 4y-2x-8=0

Find the vertex, focus, directrix and length of the latus rectum of the parabola y^2 - 4y-2x-8=0