The equation of straight line which passes through the point (a cos 3 θ, a sin 3 θ) and perpendicular to x sec θ+y operatornamecosec θ=a is

Question

The equation of straight line which passes through the point (a cos 3 θ, a sin 3 θ) and perpendicular to x sec θ+y operatornamecosec θ=a is (A) (x/a)+(y/a)=a cos θ (B) x cos θ-y sin θ=a cos 2 θ (C) x cos θ+y sin θ=a cos 2 θ (D) x cos θ-y sin θ=-a cos 2 θ

Tardigrade Admin · Accepted Answer

( x / sin θ)-( y / cos θ)=( a cos 3 θ/ sin θ)-( a sin 3 θ/ cos θ) ( x cos θ- y sin θ/ sin θ cos θ)=( a ( cos 2 θ)/ sin θ cos θ) x cos θ- y sin θ= a cos 2 θ

Q. The equation of straight line which passes through the point ( $a cos^{3} θ, a sin^{3} θ)$ and perpendicular to $x sec θ + y cosec θ = a$ is

$\frac{x}{a} + \frac{y}{a} = a cos θ$

$x cos θ - y sin θ = a cos 2 θ$

$x cos θ + y sin θ = a cos 2 θ$

$x cos θ - y sin θ = - a cos 2 θ$

$\frac{x}{s i n θ} - \frac{y}{c o s θ} = \frac{a c o s ^{3} θ}{s i n θ} - \frac{a s i n ^{3} θ}{c o s θ}$
$\frac{x c o s θ - y s i n θ}{s i n θ c o s θ} = \frac{a ( c o s 2 θ )}{s i n θ c o s θ}$
$x cos θ - y sin θ = a cos 2 θ$

Q. The equation of straight line which passes through the point (acos3θ,asin3θ) and perpendicular to xsecθ+ycosecθ=a is

ax​+ay​=acosθ

xcosθ−ysinθ=acos2θ

xcosθ+ysinθ=acos2θ

xcosθ−ysinθ=−acos2θ