Question

If straight line y = mx + c and x cos α + 7 sin α = p represent same line, then find slope of line with x axis, and length of intercept cut from y – axis.

Answer 1

y = mx + c …(i)

x cos α + 7 sin α = p

⇒ 7 sin α = -x cos α + p

Comparing equation (i) and (ii)

m = tan θ = - cot α

⇒ m = tan θ = tan(90° + α)

Thus θ = 90° + α

Slope of line = 90° + α

Thus slope of line is 90° + α and intercept is p cosecα.