Question

The value of 'm' such that mx2 – 8xy + 8y2 = 0 represents two coincident straight lines is .......

Answer 1

GIVEN :

The value of 'm' such that $mx^2-8xy + 8y^2 = 0$ represents two coincident straight lines

TO FIND :

The value of 'm' in the given two coincident straight lines

SOLUTION :

Given that $mx^2- 8xy + 8y^2 = 0$ represents two coincident straight lines

The general form of the pair of straight lines equation is  $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$

The formula for the coincident straight lines is given by :

Δ=0

$\Delta=0=\left|\begin{array}{ccc}a&h&g\\h&b&f\\g&f&c\end{array}\right|$

We have that $h^2-ab=0$

When comparing the equation $mx^2- 8xy + 8y^2 = 0$ with $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ we get the values h=-4, a=m and b=8

Substituting the values in $h^2-ab=0$

$(-4)^2-(m)(8)=0$

16-8m=0

-8m=-16

8m=16

$m=\frac{16}{8}$

m=2

∴ the value of m in the given equation $mx^2- 8xy + 8y^2 = 0$ is 2

∴  the value is m=2