A straight line passing through a fixed point | vedclass

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(B) Let the coordinates of $P$ be $(h, 0)$ and $Q$ be $(0, k)$.Since the rectangle $OPRQ$ is completed,the coordinates of $R$ are $(h, k)$.The equatio

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$3x + 2y = xy$

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(B) Let the coordinates of $P$ be $(h, 0)$ and $Q$ be $(0, k)$.Since the rectangle $OPRQ$ is completed,the coordinates of $R$ are $(h, k)$.The equation of the line passing through $P(h, 0)$ and $Q(0, k)$ is given by the intercept form:$\frac{x}{h} + \frac{y}{k} = 1$Since this line passes through the fixed point $(2, 3)$,we have:$\frac{2}{h} + \frac{3}{k} = 1$To find the locus of $R(h, k)$,we replace $h$ with $x$ and $k$ with $y$:$\frac{2}{x} + \frac{3}{y} = 1$Multiplying both sides by $xy$,we get:$2y + 3x = xy$Thus,the locus of $R$ is $3x + 2y = xy$.

$A$ straight line passing through a fixed point $(2, 3)$ intersects the coordinate axes at distinct points $P$ and $Q$. If $O$ is the origin and the rectangle $OPRQ$ is completed,then the locus of $R$ is:

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