Question

If the lines represented by $x^2+kxy+4y^2$ are coincident, then find the value of $k$.

Answer 1

The given equation is
$x^2+kxy+4y^2$ ......(i)
Comparing with $a{x}^2+2hxy+b{y}^2$, we get
$a=1,b=4,2h=k$ $\Rightarrow$ $h=\frac{k}{2}$
If the lines represented by (i) are coincident, then
$h^2=ab$
$\Rightarrow {\left(\frac{k}{2}\right)}^2=\left(1\right)\left(4\right)$
$\Rightarrow$ $k^2=16$
$\Rightarrow$ $k=\pm 4$