JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Easy

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Application +4 | -1

If the points

\left( {a,\;b} \right),\;\left( {a',\;b'} \right)

and

\left( {a - a',\;b - b'} \right)

are collinear, then

View answer and explanation

Correct option: A

ab' = a'b

Option A (

ab' = a'b

) is correct because if the points are collinear, the determinant of the matrix formed by the coordinates must be zero, leading to the given relationship.

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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