State whether the statements are true or false.
Equation of the line passing through the point (a cos3θ, a sin3θ) and perpendicular to the line x sec θ + y cosec θ = a is x cos θ – y sin θ = a sin 2θ.
Let the equation of line y=mx+c….(i)
So, slope of the above equation is m
Given equation of line is x secθ+y cosecθ=a sin 2θ.
Since the slope of the equation is m'=
Given that equation (i) is perpendicular to x secθ+y cosec θ=a sin 2θ
m*m'= -1
Putting the value of m in equation (i)we get
ysecθ=x cosec θ+c secθ
x cosec θ-y secθ=k….(ii)
If equation (ii) passes through the point (a cos3θ, a sin3θ)
(a cos3θ )cosecθ-(a sin3θ) secθ=k
a[(cos2θ-sin2θ)(cos2θ+sin2θ)]=x cosθ-ysinθ
a[cos2θ-sin2θ]=xcosθ-ysinθ
a[cos2θ]=xcos θ-y sinθ
The given statement is FALSE