Question

Choose the correct option with correct explanation:

$If \: (x - a) \: cos \: \theta + y \sin \theta \: = (x - a) \: cos \: \phi \: + y \: sin \: \phi = a \: and \: tan( \frac{ \theta}{2} ) \: = 2b \: then \:$
$(a) \: {y}^{2} = 2ax - (1 - {b}^{2} ) {x}^{2}$
$(b) \: tan \: \frac{ \theta}{2} = \frac{1}{x} (y +b x)$
$(c) \: {y}^{2} = 2bx - (1 - {a}^{2} ) {x}^{2}$
$(d) \: tan \: \frac{ \phi}{2} = \frac{1}{x} (y - bx)$
Note:
Wrong answers will be reported!!​

Answer 1

Let,

tan(2θ)=α and tan(2ϕ)=β

So that, α−β=2b

Also, cosθ=1+tan2(2θ)1−tan2(2θ)=1+α21−α2

and sinθ=1+tan2(2θ)2tan(2θ)=1+α22α

similarly, cosϕ=1+β21−β2 and sinϕ=1+β22ϕ

Therefore, we have from the given relation, (x−a)1+α2

Step-by-step explanation:

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