A straight line passing through a fixed point | vedclass

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Question

(A) Let the coordinates of $P$ be $(a, 0)$ and $Q$ be $(0, b)$.Since the line passes through $(2, 3)$,the equation of the line is $\frac{x}{a} + \frac

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$3x + 2y = xy$

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(A) Let the coordinates of $P$ be $(a, 0)$ and $Q$ be $(0, b)$.Since the line passes through $(2, 3)$,the equation of the line is $\frac{x}{a} + \frac{y}{b} = 1$.Since $(2, 3)$ lies on the line,we have $\frac{2}{a} + \frac{3}{b} = 1$.Since $OPRQ$ is a rectangle with $O(0,0)$,$P(a,0)$,and $Q(0,b)$,the coordinates of $R$ must be $(a, b)$.Let $R = (x, y)$,so $x = a$ and $y = b$.Substituting $a = x$ and $b = y$ into the equation $\frac{2}{a} + \frac{3}{b} = 1$,we get $\frac{2}{x} + \frac{3}{y} = 1$.Multiplying by $xy$,we get $2y + 3x = xy$ or $3x + 2y = xy$.

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

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