The locus of the foot of perpendicular from my focus of a hyperbola upon any tangent to the hyperbola is the auxiliary circle of the hyperbola. Consider the foci of a hyperbola as `(-3, -2)` and (5,6) and the foot of perpendicular from the focus (5, 6) upon a tangent to the hyperbola as (2, 5).
The directrix of the hyperbola corresponding to the focus (5, 6) is

Options

A. `2x+2y-1=0`
B. `2x+2y-11=0`
C. `2x+2y-7=0`
D. `2x+2y-9=0`

Answer

B

Explanation

Directrix is perpendicular to the transverse axis. Let it be
`x+y=k`.
Its distance from the center is a/e. Therefore,
`(|1+2-k|)/(sqrt2)=(5)/(2sqrt2)ork=3+(5)/(2)=(11)/(2)`