Published by:
CGP EDU Academic Team
Published on: August 13, 2026
A variable line, drawn through the point of intersection of the straight lines
= 1 and 
= 1, meets the coordinate axes in A & B. Show that the locus of the mid point of AB is the curve 2xy(a + b) = ab(x + y).
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
By family of lines 
it cuts x-axis at 
y - axis at 
. Let mid point of AB is P(h, k) ⇒ 2h = 
eliminate λ from both equations we get 2hk (a + b) = ab(h + k)
Hence locus of P(h, k) is 2xy (a + b) = ab(x + y)
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