Show that lines represented by equation x^2-2 x y-3 y^2=0 are dis… - Vidyadip

Question

Show that lines represented by equation $x^2-2 x y-3 y^2=0$ are distinct.

✓

Answer

Comparing equation $x^2-6 x y+9 y^2=0$ with $a x^2+2 h x y+b y^2=0$, we get

$

\begin{array}{c}

a=1, h=-3 \text { and } b=9 . \\

\begin{aligned}

h^2-a b & =(-3)^2-(1)(9) \\

& =9-9=0

\end{aligned}

\end{array}

$

As $h^2-a b>0$, lines represented by equation $x^2-6 x y+9 y^2=0$ are coincident.

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