Find the equation of a line which is bisected | vedclass

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Question

(A) Let the equation of the line in intercept form be $\frac{x}{a} + \frac{y}{b} = 1$.The coordinates of the points where the line intersects the $x$-

Vedclass · Accepted Answer

$\frac{x}{x_1} + \frac{y}{y_1} = 2$

Vedclass · Answer

(A) Let the equation of the line in intercept form be $\frac{x}{a} + \frac{y}{b} = 1$.The coordinates of the points where the line intersects the $x$-axis and $y$-axis are $(a, 0)$ and $(0, b)$ respectively.The midpoint of the segment intercepted between the axes is $(\frac{a}{2}, \frac{b}{2})$.Given that the line is bisected at $(x_1, y_1)$,we have $\frac{a}{2} = x_1 \implies a = 2x_1$ and $\frac{b}{2} = y_1 \implies b = 2y_1$.Substituting these values into the intercept form equation:$\frac{x}{2x_1} + \frac{y}{2y_1} = 1$Multiplying by $2$,we get $\frac{x}{x_1} + \frac{y}{y_1} = 2$.

Find the equation of a line which is bisected at the point $(x_1, y_1)$ by the axes.

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