The equation (x - 5)^2 + (x - 5)(y - 6) - 2(y | vedclass

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(C) Let $X = x - 5$ and $Y = y - 6$. The equation becomes $X^2 + XY - 2Y^2 = 0$.Factoring the quadratic expression: $X^2 + 2XY - XY - 2Y^2 = 0$$X(X +

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$C$ Two straight lines passing through the point $(5, 6)$

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(C) Let $X = x - 5$ and $Y = y - 6$. The equation becomes $X^2 + XY - 2Y^2 = 0$.Factoring the quadratic expression: $X^2 + 2XY - XY - 2Y^2 = 0$$X(X + 2Y) - Y(X + 2Y) = 0$$(X - Y)(X + 2Y) = 0$Substituting back $X = x - 5$ and $Y = y - 6$:$((x - 5) - (y - 6))((x - 5) + 2(y - 6)) = 0$$(x - y + 1)(x + 2y - 17) = 0$This represents two straight lines. Since both factors vanish at $(5, 6)$,the lines pass through the point $(5, 6)$.

The equation $(x - 5)^2 + (x - 5)(y - 6) - 2(y - 6)^2 = 0$ represents

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