Explanation
Given equation 2xy = 0
⇒ x = 0 and y = 0.
Hence these are two mutually perpendicular lines (Both axes)
A second degree homogeneous equation in x and y always represents a pair of straight lines passing through origin. But general equation of pair of straight lines, circle and conics are not homogeneous.
xy + a2 = a(x + y)
Firstly always check for pair of straight lines i.e .,Δ = 0.
Using condition Δ = 0.
To represent pair of coincident straight lines x2 + ky2 + 4xy = 0 must be perfect square or h2 = ab. Therefore, k = 4.
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