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a variable line passes through a fixed point (a,b) and meet the coordinate axes in a and b. the locus of the points of the intersection of the lines through a,b parallel coordinate axes is

a variable line passes through a fixed point (a,b) and meet the coordinate axes in a and b. the locus of the points of the intersection of the lines through a,b parallel coordinate axes is

Grade:11

1 Answers

Partha Math Expert - askIITians
askIITians Faculty 25 Points
6 years ago
If the line intersects the coordinate axes at the points (h, 0) and (0, k), thenpoints of the intersection of the lines through (h, 0) and (0, k) parallel to coordinate axes is (h,k).

The line can thus be represented by the form:\frac{x}{h} + \frac{y}{k} = 1and since it passes through (a, b) we get that\frac{a}{h} + \frac{b}{k} = 1.

Thus the locus is given by\frac{a}{x} + \frac{b}{y} = 1

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