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Let L be the line passing through the point P(1, 2) such that its intercepted segment between the co-ordinate axes is bisected at P. If L₁ is the line perpendicular to L and passing through the point (-2, 1), then the point of intersection of L and L₁ is :

Option 1)
$\left ( \frac{4}{5} ,\frac{12}{5}\right )$

Option 2)
$\left ( \frac{11}{20} ,\frac{29}{10}\right )$

Option 3)
$\left ( \frac{3}{10} ,\frac{17}{5}\right )$

Option 4)
$\left ( \frac{3}{5} ,\frac{23}{10}\right )$

Answers (2)

best_answer

As we learnt in

Intercept form of a straight line -

$\frac{x}{a}+\frac{y}{b}=1$

- wherein

$a$ and $b$ are the $x$ -intercept and $y$ -intercept respectively.

Equation of a line perpendicular to a given line -

$Bx-Ay+\lambda =0$ is the line perpendicular to $Ax+By+C =0$ .

- wherein

$\lambda$ is some other constant than $C$ .

Here $a=2, b=4$

hence equation of straight line is $\frac{x}{2}+\frac{y}{4}=1$ (intercept form)

$L:2x+y=4$

Line $\perp to L$ is $x-2y+\lambda =0$

Passing through (-2, 1)

$-2-2+\lambda =0\Rightarrow \lambda =4$

$x-2y+4=0$

$\left 2x+y-4=0 \right ]\times 2$

$4x+2y-8=0$

$\underline{x-2y+4=0}$

$x=\frac{4}{5}, y=\frac{12}{5}$

Option 1)

$\left ( \frac{4}{5} ,\frac{12}{5}\right )$

Correct option

Option 2)

$\left ( \frac{11}{20} ,\frac{29}{10}\right )$

Incorrect Option

Option 3)

$\left ( \frac{3}{10} ,\frac{17}{5}\right )$

Incorrect Option

Option 4)

$\left ( \frac{3}{5} ,\frac{23}{10}\right )$

Incorrect Option

Posted by

prateek

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JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Option no. 1

Posted by

Kumar AMAR YADAV

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