Question

# Show that the equation $$x^{2}+2xy+2y^{2}+2x+2y+1=0$$ does not represent a pair of lines.

Solution

## Comparing the equation$$x^{2}+2xy+2y^{2}+2x+2y+1=0$$ with$$ax^{2}+2hxy+by^{2}+2gx+2fy+c=0$$, we get,$$a=1, h=1, b=2, g=1, f=1, c=1$$.The given equation represents a pair of lines, if$$D=\begin{vmatrix} a & h & g \\ h & b & f \\ g & f & c \end{vmatrix}=0$$ and $$h^{2}-ab \ge 0$$Now, $$D=\begin{vmatrix} a & h & g \\ h & b & f \\ g & f & c \end{vmatrix}=\begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 1 \end{vmatrix}$$$$=1(2-1)-1(1-1)+1(1-2)$$$$=1-0-1=0$$and $$h^{2}-ab=(1)^{2}-1(2)=-1 < 0$$$$\therefore$$ given equation does not represent a pair of lines.Maths

Suggest Corrections

0

Similar questions
View More

People also searched for
View More