The equation of the lines passing through the | vedclass

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Question

(A) The given equation is $2x^2 - xy - 6y^2 + 7x + 21y - 15 = 0$.Any line parallel to the pair of lines represented by $ax^2 + 2hxy + by^2 + 2gx + 2fy

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$2x^2 - xy - 6y^2 = 0$

Vedclass · Answer

(A) The given equation is $2x^2 - xy - 6y^2 + 7x + 21y - 15 = 0$.Any line parallel to the pair of lines represented by $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ is given by $ax^2 + 2hxy + by^2 + k = 0$ for some constant $k$.Since the required lines pass through the origin $(0, 0)$,we substitute $x = 0$ and $y = 0$ into the equation $2x^2 - xy - 6y^2 + k = 0$,which gives $k = 0$.Therefore,the equation of the lines passing through the origin and parallel to the given lines is $2x^2 - xy - 6y^2 = 0$.

The equation of the lines passing through the origin and parallel to the lines represented by the equation $2x^2 - xy - 6y^2 + 7x + 21y - 15 = 0$ is:

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