Which equation represents a hyperbola with a center at open paren 0 comma 0 close paren , a vertex at open paren negative 48 comma 0 close paren , and a focus at open paren 50 comma 0 close paren ?
Answer
A
the fraction with numerator y squared and denominator 50 squared minus the fraction with numerator x squared and denominator 14 squared is equal to 1
B
the fraction with numerator y squared and denominator 48 squared minus the fraction with numerator x squared and denominator 14 squared is equal to 1
C
the fraction with numerator x squared and denominator 50 squared minus the fraction with numerator y squared and denominator 14 squared is equal to 1
D
the fraction with numerator x squared and denominator 48 squared minus the fraction with numerator y squared and denominator 14 squared is equal to 1
Explanation
The vertex and focus lie on the x-axis, so the hyperbola opens horizontally and has equation x²/a² − y²/b² = 1. The vertex gives a = 48, and c = 50 from the focus; using c² = a² + b² gives b² = 50² − 48² = 196 = 14², so the equation is x²/48² − y²/14² = 1, choice B.
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