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Find the separate equations of the lines represented by x^{2}-4 x y+3 y^{2}=0

Option: 1

x-y=0


Option: 2

x-3y=0


Option: 3

x+3y=0


Option: 4

A and B both


Answers (1)

best_answer

In this question we can use the method learnt in last example.

But as we do not have any term containing x, y or constant term, so we can easily factorize such expressions using middle term split and get the desired lines

\begin{array}{l}{x^2-4 x y+3 y^{2}=0} \\ {\Rightarrow \quad x^{2}-x y-3 x y+3 y^{2}=0} \\ {\Rightarrow \quad x(x-y)-3 y(x-y)=0} \\ {\Rightarrow \quad(x - y)(x -3y)=0} \\\text{As combined equation is (x - y)(x - 3y)=0, } \\\text{so, separate equations are x - y = 0, x - 3y = 0 }\end{array}

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Gunjita

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