If 2x - ky + 3 = 0 and 3x - y + 1 = 0 are con | vedclass

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(A) The condition for two lines $l_1x + m_1y + n_1 = 0$ and $l_2x + m_2y + n_2 = 0$ to be conjugate with respect to the hyperbola $\frac{x^2}{a^2} - \

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$6$

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(A) The condition for two lines $l_1x + m_1y + n_1 = 0$ and $l_2x + m_2y + n_2 = 0$ to be conjugate with respect to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ is $a^2l_1l_2 - b^2m_1m_2 = n_1n_2$.Given the hyperbola $5x^2 - 6y^2 = 15$,we rewrite it as $\frac{x^2}{3} - \frac{y^2}{5/2} = 1$.Here,$a^2 = 3$ and $b^2 = \frac{5}{2}$.For the lines $2x - ky + 3 = 0$ and $3x - y + 1 = 0$,we have $l_1 = 2, m_1 = -k, n_1 = 3$ and $l_2 = 3, m_2 = -1, n_2 = 1$.Substituting these values into the condition:$3(2)(3) - (\frac{5}{2})(-k)(-1) = (3)(1)$$18 - \frac{5}{2}k = 3$$15 = \frac{5}{2}k$$k = \frac{15 	imes 2}{5} = 6$.

If $2x - ky + 3 = 0$ and $3x - y + 1 = 0$ are conjugate lines with respect to the hyperbola $5x^2 - 6y^2 = 15$,then $k =$

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