Question

Find the equation of the line which is perpendicular to the line `x/a - y/b = 1` at the point where this line meets y-axis.

Answer 1

The given line is

`x/a - y/b = 1`

`=> y/b = x/a - 1`

`=> y = b/a x - b`

Slope of this line = `b/a`

Slope of the required line = `(-1)/(b/a) = (-a)/b`

Let the required line passes through the point P(0, y).

Putting x = 0 in the equation `x/a - y/b = 1` we get,

`0 - y/b = 1`

`=>` y = –b

Thus, P = (0, −b) = (x₁, y₁)

The equation of the required line is

y – y₁ = m(x – x₁)

`y + b = (-a)/b (x - 0)`

by + b² = −ax

ax + by + b² = 0