Question

$4x^2+hxy+y^2$ = 0 represent coincident lines. Find h = ?

Answer 1

To determine the value of h for which the equation $4x^2+hxy+y^2$ = 0 represents coincident lines, we need to examine the discriminant of the quadratic equation.
The given equation can be written in the form $Ax^2+2Bxy+Cy^2$ = 0, where A = 4, B = $\frac{h}{2}$, and C = 1.
The discriminant (D) of this quadratic equation is given by the formula: D = $B^2$ - AC.
For coincident lines, the discriminant should be equal to zero.
Substituting the values, we have:
D = $(\frac{h}{2})^{2}$ - 4(1)(1)
= $\frac{h^2}{4}-4$
Setting D = 0 and solving for h:
$\frac{h^2}{4}-4=0$
$\frac{h^2}{4}=4$
$h^2=16\times4$
$h^2=64$
Taking the square root of both sides:
h = ± √64
h = ± 8
Therefore, there are two possible values for h that would result in coincident lines: h = 8 or h = -8.