A variable line passes through a fixed point | vedclass

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(B) Let the equation of the variable line passing through $(a, b)$ be $\frac{x}{X} + \frac{y}{Y} = 1$. Since it passes through $(a, b)$,we have $\frac

Vedclass · Accepted Answer

$a/x + b/y = 1$

Vedclass · Answer

(B) Let the equation of the variable line passing through $(a, b)$ be $\frac{x}{X} + \frac{y}{Y} = 1$. Since it passes through $(a, b)$,we have $\frac{a}{X} + \frac{b}{Y} = 1$. The line meets the axes at $A(X, 0)$ and $B(0, Y)$. The lines drawn through $A$ and $B$ parallel to the coordinate axes intersect at point $P(h, k)$. From the geometry,$h = X$ and $k = Y$. Substituting these into the equation $\frac{a}{X} + \frac{b}{Y} = 1$,we get $\frac{a}{h} + \frac{b}{k} = 1$. Replacing $(h, k)$ with $(x, y)$,the locus is $\frac{a}{x} + \frac{b}{y} = 1$.

$A$ variable line passes through a fixed point $(a, b)$ and meets the coordinate axes at $A$ and $B$. The locus of the point of intersection of lines drawn through $A$ and $B$ parallel to the coordinate axes is:

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