First slide

Equation of line in Straight lines

Question

If $t_{1} \neq t_{2} \neq t_{3}$ and the lines $t_{1} x + y = 2 a t_{1} + a t_{1}^{3}; t_{2} x + y = 2 a t_{2} + a t_{2}^{3}; t_{3} x + y = 2 a t_{3} + a t_{3}^{3}$ are concurrent then $t_{1} + t_{2} + t_{3}$ is

Moderate

A

0
B

-1
C

1
D

2

Solution

$t_{1}, t_{2}, t_{3}$ roots of $y + x t = 2 a t + a t^{3}$

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