Question

Find k, if one of the lines given by kx² – 5xy – 3y² = 0 is perpendicular to the line x – 2y + 3 = 0

Answer 1

kx² – 5xy – 3y² = 0

Dividing by x², we get

`k - 5(y/x) - 3(y/x)^2` = 0

∴ `3(y/x)^2 + 5(y/x) - k` = 0

∴ The auxiliary equation is

3m² + 5m – k = 0   ....(1)

Since one line is perpendicular to

x – 2y + 3 = 0,

Its slope is (–2)

∴ m = –2 must satisfy equation (1)

∴ 2 – 10 – k = 0,

∴ k = 2