The normal at the point `(bt_1^2, 2bt_1)` on the parabola `y^2 = 4bx` meets the parabola again in the point `(bt_2 ^2, 2bt_2,)` then

Options

A. `t_(2)=t_(1)+2/t_(1)`
B. `t_(2)=t_(1)-2/t_(1)`
C. `t_(2)=-t_(1)+2/t_(1)`
D. `t_(2)=t_(1)-2/t_(1)`

Answer

B

Explanation

The equation of the normal to the parabola `y^(2)=4bx" at "P(bt_(1)^(2), 2bt_(1))` is
`y+t_(1)xx=2bt_(1)+bt_(1)^(3)`
If it passes thorugh `(bt_(2)^(2), 2bt_(2))`, then
`2bt_(2)+bt_(1)t_(2)^(2)=2bt_(1)+bt_(1)^(3)`
`rArr" "bt_(1)(t_(2)^(2)-t_(1)^(2))=2b(t_(1)-t_(2))`
`rArr" "t_(1)(t_(2)+t_(1))=-2rArrt_(2)=-t_(1)-2/t_(1)`