Question

find the locus of the point (tano+sino),(tano-sino)
1) ((x^2)y)^2/3 +(x(y^2))^2/3
2) (x^2)-(y^2)=xy
3) (x^2)-(y^2)=12xy
4) ((x^2)-(y^2))=16xy​

Answer 1

Answer:

x=tanθ+sinθ...(i)

y=tanθ−sinθ...(ii)

(

2

x+y

)=tanθ....adding above two equations..(iii)

(

2

x−y

)=sinθ...subtracting the above two equations..(iv)

(

2

x+y

)

2

=

cos

2

θ

sin

2

θ

..squaring eq (iii)

(

2

y+x

)

2

=

1−sin

2

θ

sin

2

θ

.. (v)

substitute the values from equation (iv) in the equation (v) we get

(x

2

−y

2

)

2

=16xy