You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

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

Open in App

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 $1.$

Suggest Corrections

Similar questions

Q. 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}

x -

intercept of

l_{2}

Q. A line parallel to

\frac{x}{5 / 3} + \frac{y}{5 / 4} = 1

has

x -

intercept

2

units and a line perpendicular to it has

y -

intercept

2

units. Then the absolute value of ratio of differences between

x -

intercepts and

y -

intercepts of perpendicular and parallel lines is

Q. A line parallel to

\frac{x}{5 / 3} + \frac{y}{5 / 4} = 1

has

x -

intercept

2

units and a line perpendicular to it has

y -

intercept

2

units. Then the absolute value of ratio of differences between

x -

intercepts and

y -

intercepts of perpendicular and parallel lines is

Q. Let

L_{1} : \frac{x - 1}{2} = \frac{y - 2}{1} = \frac{z - 3}{1}

L_{2} : \frac{x}{1} = \frac{y}{- 1} = \frac{z - 5}{3}

The equation of the line perpendicular to

L_{1}

and

L_{2}

and passing through the point of intersection of

L_{1}

and

L_{2}

Let $L_{1}$ be a straight line passing through the origin and $L_{2}$ be the straight line x + y = 1. If the intercepts made by

the circle $x^{2} + y^{2} - x + 3 y = 0$ on $L_{1}$ and $L_{2}$ are equal, then which of the following equations can represent $L_{1}$

Join BYJU'S Learning Program

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

Given line is x5/3+y5/4=1 ⇒3x+4y−5=0 Equation of l1 is 3x+4y+λ=0 It has x−intercept 2, then λ=−6 y−intercept =32 Equation of l2 is 4x−3y+δ=0 It has y−intercept 2, then δ=6 x−intercept =−32 Hence, the absolute value of the ratio is 1.