JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Easy

1 of 1

Application +4 | -1

If the points

\left(a, a^2\right)

and

(1,2)

lie in the same angular region between the lines

3 x+4 y-1=0

and

2 x+y-3=0

, then

View answer and explanation

Correct option: A

a<-3

or,

a>1

Option A (

a<-3

or,

a>1

) is correct because these values of 'a' ensure that the points (a, a²) and (1,2) lie in the same angular region between the two lines.

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\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