Portion of asymptote of hyperbola `x^2/a^2-y^2/b^2 = 1` (between centre and the tangent at vertex) in the first quadrant is cut by the line `y + lambda(x-a)=0` (lambda is a parameter) then (A) `lambda in R` (B) `lambda in (0,oo)` (C) `lambda in (-oo,0)` (D) `lambda in R-{0}`

Options

A. `lambda in R`
B. `lambda in (0, oo)`
C. `lambda in (-oo, 0)`
D. none of these

Answer

B

Explanation

The line `y+lambda(x-a)=0` will intersect the portion of the asymptote in the first quadrant only if its slope is negative.
Hence,
`-lambda lt 0`
`"or "lambda gt 0`
`therefore" "lambda in (0, oo)`