Question

find the equation of the straight line s through origin and at right angles to the lines x^2-5xy+4y^2=0​

Answer 1

SOLUTION

TO DETERMINE

The equation of the straight line s through origin and at right angles to the lines

$\sf{ {x}^{2} - 5xy + 4 {y}^{2} = 0 }$

EVALUATION

Here the pair of lines are given by the equation

$\sf{ {x}^{2} - 5xy + 4 {y}^{2} = 0 }$

We find the lines as below

$\sf{ {x}^{2} - 5xy + 4 {y}^{2} = 0 }$

$\sf{ \implies {x}^{2} - 4xy - xy + 4 {y}^{2} = 0 }$

$\sf{ \implies x(x - 4y) - y(x - 4y) = 0 }$

$\sf{ \implies (x - 4y) (x - y) = 0 }$

So given pair of lines are :

x - 4y = 0

x - y = 0

Now the equation of the line perpendicular to the line x - 4y = 0 and passing through the origin is 4x + y = 0

Again the equation of the line perpendicular to the line x - y = 0 and passing through the origin is x + y = 0

Hence the required equation is

$\sf{(4x + y)(x + y) = 0}$

$\sf{ \implies \: 4x (x + y) + y( x+ y)= 0}$

$\sf{ \implies \: 4 {x}^{2} + 4xy + xy + {y}^{2} = 0}$

$\sf{ \implies \: 4 {x}^{2} + 5xy + {y}^{2} = 0}$

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Answer 2

Answer:

Step-by-step explanation:

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