Family of lines $\lambda x+3 y-6=0(\lambda$ is a real parameter $)$ intersect the lines $x-2 y+3=0$ and $x-y+1=0$ in $P$ and $Q$, then locus of the middle point of $P Q$ is

JEE MATHEMATICS MCQ: STRAIGHT LINES

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Family of lines

\lambda x+3 y-6=0(\lambda

is a real parameter

)

intersect the lines

x-2 y+3=0

and

x-y+1=0

P

and

Q

, then locus of the middle point of

P Q

View answer and explanation

Correct option: D

4 x+3 y=4

The correct answer is D (

4x+3y=4

) because the locus of the midpoint of PQ is found by using the equation of the chord with a given midpoint and the fact that the family of lines passes through a fixed point.

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