JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Easy

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Analyzing +4 | -1

t_1, t_2

and

t_3

are distinct, the points

\left(t_1, 2 a t_1+a t_1^3\right)

\left(t_2, 2 a t_2+a t_2^3\right)

and

\left(t_3, 2 a t_3+a t_3^3\right)

are collinear if

View answer and explanation

Correct option: C

t_1+t_2+t_3=0

Option C is correct. The points are collinear if the determinant formed by their coordinates is zero, which simplifies to t1 + t2 + t3 = 0.

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\left\{ {a{t_1}{t_2},\;a\left( {{t_1} + {t_2})\} ,\{ a{t_2}{t_3},a({t_2} + {t_3}} \right)} \right\},\;\left\{ {a{t_3}{t_1},\;a\left( {{t_3} + {t_1}} \right)} \right\}

y = 2\;x + 4

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{x^2} + {y^2} + 2xy - 8ax - 8ay - 9{a^2} = 0

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\left( {{x^2} + 7xy + 2{y^2}} \right)\left( {y - 1} \right) = 0