JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Hard

1 of 1

Application +4 | -1

The lines

x\cos \alpha + y\sin \alpha = {p_1}

and

x\cos \beta + y\sin \beta = {p_2}

will be perpendicular, if

View answer and explanation

Correct option: C

\left| {\alpha - \beta } \right| = \frac{\pi }{2}

Option C (

\left| {\alpha - \beta } \right| = \frac{\pi }{2}

) is correct because the lines are perpendicular when the difference in their angles is

\frac{\pi }{2}

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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

6x = 3y + 5

{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