The asymptotes of the hyperbola `x y=h x+k y` are (1)`x-k=0` and `y-h=0` `(2)x+h=0` and `y+k=0` (3)`x-k=0` and `y+h=0` `(4)x+k=0` and `y-h=0`

Options

A. x - k = 0 and y - h = 0
B. x + h = 0 and y + k = 0
C. x - k = 0 and y + h = 0
D. x + k = 0 and y - h = 0

Answer

A

Explanation

The given hyperbola is
`xy-hx-ky=0" (1)"`
The equation of asymptotes is given by
`xy-hx-ky+c=0" (2)"`
Equation (2) gives a pair of straight lines. So,
`|(A,H,G),(H,B,F),(G,F,C)|=0`
`or|(0,1//2,-h//2),(1//2,0,-k//2),(-h//2,-k//2,c)|=0`
`"or "(hk)/(8)+(hk)/(8)-(c)/(4)=0`
`"or "c=hk`
Hence, the asymptotes are
`xy-hx-ky+hk=0`
`"or "(x-k)(y-h)=0`