Find the foci of the hyperbola.
-$$x ^ { 2 } - y ^ { 2 } = 50$$
A) (10, 0), (-10, 0)
B) (5, 0), (-5, 0)
C) (0, 5), (0, -5)
D) (0, 10), (0, -10)

Question

Quizplus · Accepted Answer

The given equation of the hyperbola is in the form $x^2 - y^2 = 50$, which can be rewritten as $\frac{x^2}{50} - \frac{y^2}{50} = 1$, indicating it's a horizontal hyperbola centered at the origin. The distance of each focus from the center is given by $c = \sqrt{a^2 + b^2}$, where $a^2 = 50$ and $b^2 = 50$. Thus, $c = \sqrt{50 + 50} = \sqrt{100} = 10$. Therefore, the foci are at $(\pm10, 0)$.

Find the Foci of the Hyperbola x2−y2=50x ^ { 2 } - y ^ { 2 } = 50x2−y2=50

Find the Foci of the Hyperbola $x ^ { 2 } - y ^ { 2 } = 50$