JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Easy

1 of 1

Analyzing +4 | -1

A rectangle

A B C D

has its side

A B

parallel to line

y=x

and vertices

A, B

and

D

lie on

y=1, x=2

and

x=-2

respectively. Locus of vertex

C

View answer and explanation

Correct option: C

y=5

The correct answer is C (

y=5

) because the locus of vertex C is found by expressing the coordinates of C in terms of a parameter and eliminating it.

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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

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