First slide

Pair of straight lines

Question

If $x^{2} - y^{2} = 0, lx + 2 y = 1$ form a isosceles triangle, then $l =$

Easy

A

0
B

1
C

2
D

4

Solution

The given lines are
$x + y = 0$ …… (1)
$x - y = 0$ …… (2)
And
$lx + 2 y = 1$ …… (3)
Equations (1) and (2) represents two perpendicular lines, and the third line makes an angle with the line (1) and line (2)
Hence,
$\begin{array}{r} \tan 45 ° = |\frac{m_{1} - m_{2}}{1 + m_{1} m_{2}}| \\ = |\frac{- \frac{l}{2} - 1}{1 - \frac{l}{2}}| \\ = |\frac{l + 2}{2 - l}| \end{array}$

It implies that $l = 0$

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