Find the standard form of the equation of the following hyperbola.
$10 x ^ { 2 } - 6 y ^ { 2 } = 60$
A) $\frac { x ^ { 2 } } { ( \sqrt { 6 } ) ^ { 2 } } - \frac { y ^ { 2 } } { ( \sqrt { 10 } ) ^ { 2 } } = 1$
B) $\frac { x ^ { 2 } } { 10 ^ { 2 } } - \frac { y ^ { 2 } } { 6 ^ { 2 } } = 1$
C) $\frac { y ^ { 2 } } { ( \sqrt { 10 } ) ^ { 2 } } - \frac { x ^ { 2 } } { ( \sqrt { 6 } ) ^ { 2 } } = 1$
D) $\frac { y ^ { 2 } } { ( \sqrt { 6 } ) ^ { 2 } } - \frac { x ^ { 2 } } { ( \sqrt { 10 } ) ^ { 2 } } = 1$
E) $\frac { x ^ { 2 } } { ( \sqrt { 10 } ) ^ { 2 } } - \frac { y ^ { 2 } } { ( \sqrt { 6 } ) ^ { 2 } } = 1$

Question

Quizplus · Accepted Answer

The equation of the hyperbola is in the form $\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$, where $a$ is the distance from the center to the vertices and $b$ is the distance from the center to the co-vertices. In this case, $a = \sqrt { 6 }$ and $b = \sqrt { 10 }$, so the standard form of the equation is $\frac { x ^ { 2 } } { ( \sqrt { 6 } ) ^ { 2 } } - \frac { y ^ { 2 } } { ( \sqrt { 10 } ) ^ { 2 } } = 1$.

Find the Standard Form of the Equation of the Following 10x2−6y2=6010 x ^ { 2 } - 6 y ^ { 2 } = 6010x2−6y2=60

Find the Standard Form of the Equation of the Following $10 x ^ { 2 } - 6 y ^ { 2 } = 60$