Question

The product of the perpendicular from two foci on any tangent to the hyperbola `x^2/a^2-y^2/b^2=1` is (A) `a^2` (B) `(b/a)^2` (C) `(a/b)^2` (D) `b^2`

Answer 1

The hyperbola is on minor axis=>`y=b`
The two focii are`S_1(ae,0)` and `S_2(-ae,0)`
Let tangent be=>`ax+by+c=0`
Perpendicular length from focii to tangent=>`S_1(b) AND S_2(b)`
Their product=`b^2`