Question

find the separate equation of the lines represented by 5x^2-9xy+4y^2=0​

Answer 1

SOLUTION

TO DETERMINE

The separate equation of the lines represented by

$\sf{5 {x}^{2} - 9xy + 4 {y}^{2} = 0}$

EVALUATION

Here the given equation is

$\sf{5 {x}^{2} - 9xy + 4 {y}^{2} = 0}$

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

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

$\sf{ \implies \: 5x(x - y) - 4y(x - y)= 0}$

$\sf{ \implies \: (x - y) (5x - 4y)= 0}$

Hence the separate equation of the lines represented by

• x - y = 0

• 5x - 4y = 0