JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Easy

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Analyzing +4 | -1

Straight lines

\frac{x}{a}+\frac{y}{b}=1, \frac{x}{b}+\frac{y}{a}=1, \frac{x}{a}+\frac{y}{b}=2

and

\frac{x}{b}+\frac{y}{a}=2

form a rhombus of area (in square units)

View answer and explanation

Correct option: D

\frac{a^2 b^2}{\left|a^2-b^2\right|}

Option D (

\frac{{a^2 b^2}}{{\left|a^2-b^2\right|}}

) is correct because it represents the area of the rhombus formed by the given lines, calculated using the determinant method.

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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

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