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Byju's Answer

Standard XIII

Mathematics

Condition for Two Lines to Be Perpendicular

Let l1 be par...

Question

Let $l_{1}$ be parallel to $\frac{x}{5 / 3} + \frac{y}{5 / 4} = 1$ and $l_{2}$ be perpendicular to it. If $l_{1}$ has $x -$ intercept equals to $2$ units and $l_{2}$ has $y -$ intercept equals to $2$ units, then the absolute value of the ratio of $y -$ intercept of $l_{1}$ to $x -$ intercept of $l_{2}$ is

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Solution

Given line is $\frac{x}{5 / 3} + \frac{y}{5 / 4} = 1$
$\Rightarrow 3 x + 4 y - 5 = 0$
Equation of $l_{1}$ is
$3 x + 4 y + λ = 0$
It has $x -$ intercept $2$ , then
$λ = - 6$
$y -$ intercept $= \frac{3}{2}$

Equation of $l_{2}$ is
$4 x - 3 y + δ = 0$
It has $y -$ intercept $2$ , then
$δ = 6$
$x -$ intercept $= - \frac{3}{2}$

Hence, the absolute value of the ratio is $1.$

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Let l1 be parallel to x5/3+y5/4=1 and l2 be perpendicular to it. If l1 has x−intercept equals to 2 units and l2 has y−intercept equals to 2 units, then the absolute value of the ratio of y−intercept of l1 to x−intercept of l2 is

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