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Please help with the question: A variable straight line throigh the poin 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 2xy(a+b)=ab(x+y).

Please help with the question:
 
A variable straight line throigh the poin 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 2xy(a+b)=ab(x+y).

Grade:

1 Answers

Shobhit Varshney IIT Roorkee
askIITians Faculty 33 Points
6 years ago
Hi,

Equation of family of lines passing through intersection of these two lines is given by:

(x/a + y/b -1) + q (x/b + y/a -1) = 0
(1/a + q/b)x + (1/b + q/a)y -(1+q) = 0

Find the coordinates where this equation intersects the axes and find the mid point of the line connecting the two points.

Eliminate q from the coordinates of the mid point to find out the locus of the mid point.

thanks

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