The equation x^2-y^2+ax+b=0 represents a pair | vedclass

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(D) The general equation of a second-degree curve is $Ax^2 + 2Hxy + By^2 + 2Gx + 2Fy + C = 0$. This represents a pair of straight lines if the determi

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$6, 9$

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(D) The general equation of a second-degree curve is $Ax^2 + 2Hxy + By^2 + 2Gx + 2Fy + C = 0$. This represents a pair of straight lines if the determinant $\Delta = \begin{vmatrix} A & H & G \ H & B & F \ G & F & C \end{vmatrix} = 0$. Comparing $x^2 - y^2 + ax + b = 0$ with the general form,we have $A=1, B=-1, C=b, H=0, G=\frac{a}{2}, F=0$. Substituting these values into the determinant condition: $\begin{vmatrix} 1 & 0 & \frac{a}{2} \ 0 & -1 & 0 \ \frac{a}{2} & 0 & b \end{vmatrix} = 0$. Expanding along the second row: $-1 	imes (1 	imes b - \frac{a}{2} 	imes \frac{a}{2}) = 0$. $-1 	imes (b - \frac{a^2}{4}) = 0$ $\Rightarrow b - \frac{a^2}{4} = 0$ $\Rightarrow a^2 = 4b$. Checking the options: For $(6, 9)$,$6^2 = 36$ and $4 	imes 9 = 36$. Thus,the ordered pair $(6, 9)$ satisfies the condition.

The equation $x^2-y^2+ax+b=0$ represents a pair of lines for the ordered pair $(a, b) =$

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