A line of slope `lambda(0 < lambda < 1)` touches the parabola `y+3x^2=0` at `Pdot` If `S` is the focus and `M` is the foot of the perpendicular of directrix from `P` , then `tan/_M P S` equals (a)`2lambda` (b) `(2lambda)/(-1+lambda^2)` (c) `(1-lambda^2)/(1+lambda^2)` (d) none of these

Options

A. `2lamda`
B. `(2lamda)/(-1+lamda^(2))`
C. `(1-lamda^(2))/(1+lamda^(2))`
D. none of these

Answer

B

Explanation

(2)
Slope of line `=lamda=tantheta`
`:." "tan(angleMPS)=tan((pi)/(2)-theta)=tan(pi-2theta)`
`=-tan2theta=(2lamda)/(lamda^(2)-1)`