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Question

(C) The equation of any line passing through the intersection of $L_1: 3x - y + 2 = 0$ and $L_2: 5x - 2y + 7 = 0$ is given by $L_1 + \lambda L_2 = 0$.

Vedclass · Accepted Answer

$x = 3$

Vedclass · Answer

(C) The equation of any line passing through the intersection of $L_1: 3x - y + 2 = 0$ and $L_2: 5x - 2y + 7 = 0$ is given by $L_1 + \lambda L_2 = 0$.$(3x - y + 2) + \lambda (5x - 2y + 7) = 0$$(3 + 5\lambda)x - (1 + 2\lambda)y + (2 + 7\lambda) = 0$For a line to have an infinite slope,the coefficient of $y$ must be zero.$1 + 2\lambda = 0 \implies \lambda = -1/2$Substituting $\lambda = -1/2$ into the equation:$(3x - y + 2) - \frac{1}{2}(5x - 2y + 7) = 0$Multiply by $2$:$2(3x - y + 2) - (5x - 2y + 7) = 0$$6x - 2y + 4 - 5x + 2y - 7 = 0$$x - 3 = 0 \implies x = 3$.

The equation of the straight line passing through the point of intersection of the straight lines $3x - y + 2 = 0$ and $5x - 2y + 7 = 0$ and having an infinite slope is:

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