JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Easy

1 of 1

Application +4 | -1

A line is drawn from the point

P(\alpha, \beta)

making an angle

\theta

with the positive direction of

X

-axis to meet the line

a x+b y+c=0

Q

. The length of

P Q

View answer and explanation

Correct option: A

-\frac{a \alpha+b \beta+c}{a \cos \theta+b \sin \theta}

Option A (

-\frac{{a \alpha+b \beta+c}}{{a \cos \theta+b \sin \theta}}

) is correct because it represents the length PQ derived from the equation of a line and its intersection with another line.

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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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x+3 y=7

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