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(C) Let the line intersect the $x$-axis at $A(a, 0)$ and the $y$-axis at $B(0, b)$.Given that the point $P(-4, 3)$ divides the segment $AB$ in the rat

Vedclass · Accepted Answer

$9x - 20y + 96 = 0$

Vedclass · Answer

(C) Let the line intersect the $x$-axis at $A(a, 0)$ and the $y$-axis at $B(0, b)$.Given that the point $P(-4, 3)$ divides the segment $AB$ in the ratio $5 : 3$ internally.Using the section formula,the coordinates of $P$ are given by:$P = \left( \frac{5(0) + 3(a)}{5 + 3}, \frac{5(b) + 3(0)}{5 + 3} \right) = \left( \frac{3a}{8}, \frac{5b}{8} \right)$.Equating this to $(-4, 3)$,we get:$\frac{3a}{8} = -4$ $\Rightarrow 3a = -32$ $\Rightarrow a = -\frac{32}{3}$.$\frac{5b}{8} = 3$ $\Rightarrow 5b = 24$ $\Rightarrow b = \frac{24}{5}$.The intercept form of the line is $\frac{x}{a} + \frac{y}{b} = 1$.Substituting the values of $a$ and $b$:$\frac{x}{(-32/3)} + \frac{y}{(24/5)} = 1$$-\frac{3x}{32} + \frac{5y}{24} = 1$.Multiplying by $96$ (the $LCM$ of $32$ and $24$):$-9x + 20y = 96$$9x - 20y + 96 = 0$.

The equation of the line which passes through the point $(-4, 3)$ and whose portion intercepted between the axes is divided internally in the ratio $5 : 3$ by this point is:

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