JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Easy

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Application +4 | -1

If the points

(1,2)

and

(3,4)

are to be on the same side of the line

3 x-5 y+a=0

then

View answer and explanation

Correct option: D

a<7

(or)

a>11

Option D (a<7 or a>11) is correct because for the points to be on the same side of the line, the product of the expressions obtained by substituting the points into the line equation must be greater than 0, leading to the inequality (a-7)(a-11) > 0.

More Questions from STRAIGHT LINES

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If the three lines

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

and

a x+y=r

form a right-angled triangle then :
The orthocentre of the triangle whose vertices are

\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\}

is
The distance between the parallel lines

y = 2\;x + 4

and

6x = 3y + 5

is The distance between the pair of lines given by

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

is Find the image of the point

(3,8)

with respect of the line

x+3 y=7

assuming the line to be plane mirror: The centroid of the triangle whose three sides are given by the combined equation

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