JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Easy

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\left| {\begin{array}{cccccccccccccccccccc} {{x_1}}&{{y_1}}&1\\ {{x_2}}&{{y_2}}&1\\ {{x_3}}&{{y_3}}&1 \end{array}} \right| = 0

, then the points

\left( {{x_1},{y_1}} \right),\;\left( {{x_2},\;{y_2}} \right)

and

\left( {{x_3},{y_3}} \right)

are

View answer and explanation

Correct option: D

None of the above

Option D (None of the above) is correct because if the determinant is zero, the points are collinear, not vertices of any triangle.

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a x+y=r

\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