Question

Equation of the rectangular hyperbola whose focus is `(1,-1)` and the corresponding directrix is `x-y+1=0`
A. `x^(2)-y^(2)=1`
B. `xy=1`
C. `2xy-4x+4y+1=0`
D. `2xy+4x-4y-1=0`

Answer 1

Correct Answer - C
Eccentricity of rectangular hyperbola is `sqrt2`.
So, equation of hyperbola is
`sqrt((x-1)^(2)+(y+1)^(2))=sqrt2(|x-y+1|)/(sqrt(1^(2)+(-1)^(2)))`
`rArr" "(x-1)^(2)+(y+1)^(2)=(x-y+1)^(2)`
`rArr" "2xy-4x+4y+1=0`