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0 votes
10.3k views
in Mathematics by (53.1k points)

A variable straight line through the point of intersection of the lines

x/a + y/b = 1 and x/b + y/a = 1

meets the coordinate axes at A and B. Show that the locus of the midpoint of AB is the curve

2(a + b)xy = ab(x + y)

1 Answer

+1 vote
by (53.3k points)
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Best answer

Equation of any line through the intersection of the given lines is of the form

This line meets the x-axis at

Let M(x1, y1) be the midpoint of (bar)AB. Therefore

Therefore, the locus of (x1, y1) is 

2(a +b)xy =  (ab)(x + y)

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