The length of the x-intercept made by the pai | vedclass

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(C) The given equation is $2x^2 + xy - 6y^2 - 2x + 17y - 12 = 0$. Comparing this with the general equation of a pair of lines $ax^2 + 2hxy + by^2 + 2g

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$5$

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(C) The given equation is $2x^2 + xy - 6y^2 - 2x + 17y - 12 = 0$. Comparing this with the general equation of a pair of lines $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$,we get $a = 2$,$g = -1$,and $c = -12$. The length of the $x$-intercept made by the pair of lines is given by the formula $\frac{2\sqrt{g^2 - ac}}{a}$. Substituting the values,we get: $	ext{Length} = \frac{2\sqrt{(-1)^2 - 2(-12)}}{2} = \frac{2\sqrt{1 + 24}}{2} = \sqrt{25} = 5$. Thus,the length of the $x$-intercept is $5$.

The length of the $x$-intercept made by the pair of lines $2x^2 + xy - 6y^2 - 2x + 17y - 12 = 0$ is

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