Question

Find the separate equations of the lines represented by following equation:

xy + y² = 0

Answer 1

Comparing the equation xy + y² = 0 with ax² + 2hxy + by² = 0, we get,

a = 0, 2h = 1, b = 1

Let m₁ and m₂ be the slopes of the lines

represented by xy + y² = 0

Now required lines are perpendicular to these lines

∴ their slopes are \(\cfrac{-1}{m_1}\) and \(\cfrac{-1}{m_2}\).

Since these lines are passing through the origin, their separate equations are

∴ separate equations of the lines are y = 0 and

3x² + 8xy + 5y² = 0.

x + y = 0.

Let m₁ and m₁ be the slopes of these lines. 

Then m₁ = 0 and m₂ = -1

Let m₁ and m₂ be the slopes of these lines. 

Then m₁ = 0 and m₂ = -1

Since these lines are passing through the origin, their separate equations are x = 0 and y = x,

i.e. x – y = 0 

∴ their combined equation is 

x(x – y) = 0 

x² – xy = 0.