The equation to the straight line passing through the point `(a "cos"^(3) theta, a "sin"^(3) theta)` and perpendicular to the line `x "sec" theta + y"cosec" theta = a` is

Options

A. `x "cos " theta-y "sin" theta = a "cos" 2theta`
B. `x "cos " theta+y "sin" theta = a "cos" 2theta`
C. `x "sin" theta+y "cos" theta = a "cos" 2theta`
D. none of these

Answer

A

Explanation

The line perpendicular to `x "sec" theta + y "cosec" theta = a` is
`x "cosec" theta-y "sec"theta = lambda`
This line passes through the point `(a "cos"^(3) theta, a "sin"^(3) theta)`. Then,
`(a "cos"^(3) theta)"cosec" theta -(a "sin"^(3)theta) "sec" theta=lambda`
`"or " lambda = a(( "cos"^(3) theta)/("sin"theta) - ("sin"^(3) theta)/("cos"theta))`
`= a(( "cos"2 theta)/("cos"theta "sin"theta))`