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10-2. Parabola, Ellipse, Hyperbola
easy
જેની નાભિઓ $(-2, 0)$ અને $(2, 0)$ હોય, અને ઉત્કેન્દ્રતા $2$ હોય તેવા અતિવલયનું સમીકરણ :
A
$-3x^2 + y^2 = 3$
B
$x^2 - 3y^2 = 3$
C
$3x^2 - y^2 = 3$
D
$-x^2 + 3y^2 = 3$
Solution
Let the equation of the hyperbola is
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
where $2 ae =4$ and $e =2 \Rightarrow a =1$
$a ^2 e ^2= a ^2+ b ^2 \Rightarrow 4=1+ b ^2$
$b^2=3$
$\therefore$ equation of hyperbola is $\frac{x^2}{1}-\frac{y^2}{3}=1$
$3 x^2-y^2-3=0$
Standard 11
Mathematics
