If the equation given by hxy + 10x + 6y + 4 = | vedclass

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(B) The general equation of a second-degree curve is $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$.Comparing $hxy + 10x + 6y + 4 = 0$ with the general form

Vedclass · Accepted Answer

$30$

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(B) The general equation of a second-degree curve is $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$.Comparing $hxy + 10x + 6y + 4 = 0$ with the general form,we get $a = 0, b = 0, 2h' = h \Rightarrow h' = h/2, g = 5, f = 3, c = 4$.For the equation to represent a pair of lines,the determinant must be zero:$\Delta = \begin{vmatrix} a & h' & g \ h' & b & f \ g & f & c \end{vmatrix} = 0$$\begin{vmatrix} 0 & h/2 & 5 \ h/2 & 0 & 3 \ 5 & 3 & 4 \end{vmatrix} = 0$$0(0 - 9) - \frac{h}{2}(2h/2 - 15) + 5(3h/2 - 0) = 0$$-\frac{h}{2}(h - 15) + \frac{15h}{2} = 0$$-\frac{h^2}{2} + \frac{15h}{2} + \frac{15h}{2} = 0$$-\frac{h^2}{2} + 15h = 0$$-h^2 + 30h = 0 \Rightarrow h(30 - h) = 0$Therefore,$h = 0$ or $h = 30$.

If the equation given by $hxy + 10x + 6y + 4 = 0$ represents a pair of lines,then $h$ is equal to

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