Question

please this question​

Answer 1

Answer :

x = a cot θ - b cosec θ... (1)

y = a cot θ + b cosec θ... (2)

Adding these equations, we get :

x + y = 2a cot θ

$\tt {\cot \theta= \frac{x + y}{2a}} ...(3)$

Subtracting (2) from (1),

y - x = 2b cosec θ

So,

$\tt{ \cosec \theta = \frac{y - x}{2b} ...(4)}$

Now,

We know that,

cosec^2 θ - cot^2 θ = 1

Eliminating θ,

$\tt{(\frac{y - x}{2b}) {}^{2} - (\frac{x + y}{2a}) {}^{2} = 1}$

Hence, We get :

$\tt{\frac{(y - x) {}^{2} }{4 {b}^{2} } - \frac{(x + y) {}^{2} }{4 {a {}^{2} }}^{} } = 1$

or

$\tt{(\frac{y - x{}^{2} }{ {b}^{} }) - (\frac{(x + y) {}^{2} }{ {a {}^{} }}^{} }) = 4$

Hope it helps!