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.