`lx +my = 1` is the equation of the chord PQ of `y^(2) = 4x` whose focus is S. If PS and QS meet the parabola again at R and T respectively, then slope of RT is (a) -1/m (b) 1/m (c) 2/m (d) none of the above

Options

A. `-(1)/(m)`
B. `(l)/(m)`
C. `(2)/(m)`
D. none of these

Answer

A

Explanation

Let us take P and Q as `t_(1)` and `t_(2)` respectively.
Equation to PQ is `-2x +y (t_(1)+t_(2)) = 2t_(1)t_(2)`
Comparing with `lx +my =1`, we get
`t_(1) + t_(2) =- (2m)/(l)` and `t_(1)t_(2) =- (1)/(l)`
R is `((1)/(t_(1)^(2)),-(2)/(t_(1)))` and T is `((1)/(t_(2)^(2)),-(2)/(t_(2))) [ :' PSR` and QST are focal chords]
Slope of `RT (2((1)/(t_(2))-(1)/(t_(1))))/((1)/(t_(1)^(2))-(1)/(t_(2)^(2))) =-(2t_(1)t_(2))/(t_(1)+t_(2)) =(-2(-(1)/(l)))/(-(2m)/(l)) =-(1)/(m)`