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The equation to the straight line passin...

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

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

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The correct Answer is:
A
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))`
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