Find the eccentricity e of the hyperbola.
-$x ^ { 2 } - y ^ { 2 } = 49$
A) $\sqrt { 7 }$
B) 1
C) 0
D) $\sqrt { 2 }$

Question

Quizplus · Accepted Answer

The eccentricity $e$ of a hyperbola is given by $e = \sqrt{1 + \frac{b^2}{a^2}}$, where $a^2$ and $b^2$ are the coefficients of $x^2$ and $y^2$ respectively, with the standard form being $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. For the given equation $x^2 - y^2 = 49$, we can rewrite it as $\frac{x^2}{49} - \frac{y^2}{49} = 1$, implying $a^2 = b^2 = 49$. Thus, $e = \sqrt{1 + \frac{49}{49}} = \sqrt{2}$.

Find the Eccentricity E of the Hyperbola x2−y2=49x ^ { 2 } - y ^ { 2 } = 49x2−y2=49

Find the Eccentricity E of the Hyperbola $x ^ { 2 } - y ^ { 2 } = 49$