Let S = [ ( x,y ) R^2:y^2 1 + r - x^2 1 - r ;r 1.] Then S represents :

Question

Let S = $$\left\{ {\left( {x,y} \right) \in {R^2}:{{{y^2}} \over {1 + r}} - {{{x^2}} \over {1 - r}}} \right\};r \ne  \pm 1.$$ Then S represents :

Accepted Answer

$${{{y^2}} \over {1 + r}} - {{{x^2}} \over {1 - r}} = 1$$

for r > 1,     $${{{y^2}} \over {1 + r}} + {{{x^2}} \over {1 - r}} = 1$$

$$e = \sqrt {1 - \left( {{{r - 1} \over {r + 2}}} \right)} $$

$$ = \sqrt {{{\left( {r + 1} \right) - \left( {r - 1} \right)} \over {\left( {r + 1} \right)}}} $$

$$ = \sqrt {{2 \over {r + 1}}}  = \sqrt {{2 \over {r + 1}}} $$

Solutions · 1