PSQ is a focal chord of a parabola whose focus is S and vertex is A. PA and QA are produced to meet the directrix in R and T, respectively. Then `angleRST=``

Options

A. `90^(@)`
B. `60^(@)`
C. `45^(@)`
D. `30^(@)`

Answer

A

Explanation

Let `P(at_(1)^(2), 2at_(1)), Q(at_(2)^(2), 2at_(2))` be the end-points of a focal chord PSQ of the parabola `y^(2)=4ax`. The equations of

AP and AQ are `y=2/t_(1)" x and y"=2/t_(2)" x respectively"`. These two meet the directrix x= - a at R`(-a,(-2a)/t_(1))" and T"(-a, (-2a)/t_(2))` respectively.
`:." "m_(1)="Slope of RS"=1/t_(1), m_(2)="Slope of ST"=1/t_(2)`
`:." "m_(1)m_(2)=1/(t_(1)t_(2))=-1" "[becausePQ" is a focal chord"becauset_(1)t_(2)=-1]`
Hence, `/_RST=90^(@)`.