Question

Find the value of $k$, if the lines represented by $k(x^2+y^2)=8xy$ are coincident.

Answer 1

For the homogeneous equation of pair of straight lines $a{x}^2+b{y}^2+2hxy=0$ , condition of coincidency is

$h^2-ab=0$

Now the given equation is,

$k(x^2+y^2)=8xy$

$k{x}^2+k{y}^2-8xy=0$

Lines represented by the above equation will be coincident if

$(-4{)}^2-k^2=0$

$k^2=16$

$k=\pm 4$