JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Easy

1 of 1

Application +4 | -1

If a straight line through the point

P(3,5)

makes an angle

\frac{\pi}{6}

with

x

-axis and meets the lines

2 x+y+5=0 \,\& \,3 x-2 y+7=0

Q \,\&\, R

then

\frac{P Q}{P R}=

View answer and explanation

Correct option: C

\frac{2(12 \sqrt{3}-8)}{6 \sqrt{3}+3}

Option C,

\frac{{2(12 \sqrt{{3}}-8)}}{{6 \sqrt{{3}}+3}}

, is the correct ratio of PQ to PR, calculated by finding the intersection points of the line with the given lines and using the distance formula.

More Questions from STRAIGHT LINES

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x-3 y=p, a x+2 y=q

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

6x = 3y + 5

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

(3,8)

x+3 y=7

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