AnswersGeometryEquations of Hyperbolas (continued)

Equations of Hyperbolas (continued) — Quiz Answers

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3

The vertices of a hyperbola are located at open paren 3 comma negative 6 close paren and open paren 3 comma 6 close paren The foci of the same hyperbola are located at open paren 3 comma negative 10 close paren and open paren 3 comma 10 close paren What is the equation of the hyperbola?

A
the fraction with numerator y squared and denominator 64 minus the fraction with numerator open paren x minus 3 close paren squared and denominator 36 is equal to 1
B
the fraction with numerator open paren y minus 3 close paren squared and denominator 64 minus the fraction with numerator x squared and denominator 36 is equal to 1
C
the fraction with numerator open paren y minus 3 close paren squared and denominator 36 minus the fraction with numerator x squared and denominator 64 is equal to 1
D
the fraction with numerator y squared and denominator 36 minus the fraction with numerator open paren x minus 3 close paren squared and denominator 64 is equal to 1
4

What is the center of the hyperbola whose equation is the fraction with numerator open paren y plus 3 close paren squared and denominator 81 minus the fraction with numerator open paren x minus 6 close paren squared and denominator 89 is equal to 1 ?

A
open paren 6 comma negative 3 close paren
B
open paren negative 3 comma 6 close paren
C
open paren 3 comma negative 6 close paren
D
open paren negative 6 comma 3 close paren
5

What are the vertices of the hyperbola whose equation is the fraction with numerator open paren y plus 6 close paren squared and denominator 81 minus the fraction with numerator open paren x plus 8 close paren squared and denominator 49 is equal to 1 ?

A
open paren negative 17 comma negative 6 close paren and open paren 1 comma negative 6 close paren
B
open paren negative 8 comma negative 13 close paren and open paren negative 8 comma 1 close paren
C
open paren negative 8 comma negative 15 close paren and open paren negative 8 comma 3 close paren
D
open paren negative 15 comma negative 6 close paren and open paren negative 1 comma negative 6 close paren
6

The vertices of a hyperbola are located at open paren negative 4 comma 1 close paren and open paren 4 comma 1 close paren The foci of the same hyperbola are located at open paren negative 5 comma 1 close paren and open paren 5 comma 1 close paren What is the equation of the hyperbola?

A
the fraction with numerator x squared and denominator 9 minus the fraction with numerator open paren y plus 1 close paren squared and denominator 16 is equal to 1
B
the fraction with numerator x squared and denominator 16 minus the fraction with numerator open paren y minus 1 close paren squared and denominator 9 is equal to 1
C
the fraction with numerator x squared and denominator 9 minus the fraction with numerator open paren y minus 1 close paren squared and denominator 16 is equal to 1
D
the fraction with numerator x squared and denominator 16 minus the fraction with numerator open paren y plus 1 close paren squared and denominator 9 is equal to 1
7

A hyperbola has its foci at open paren 7 comma 5 close paren and open paren 7 comma negative 5 close paren A directrix of the hyperbola is y is equal to 16 fifths What is the equation of the hyperbola?

A
the fraction with numerator y squared and denominator 16 minus the fraction with numerator open paren x minus 7 close paren squared and denominator 9 is equal to 1
B
the fraction with numerator x squared and denominator 16 minus the fraction with numerator open paren y minus 7 close paren squared and denominator 9 is equal to 1
C
the fraction with numerator x squared and denominator 9 minus the fraction with numerator open paren y minus 7 close paren squared and denominator 16 is equal to 1
D
the fraction with numerator y squared and denominator 9 minus the fraction with numerator open paren x minus 7 close paren squared and denominator 16 is equal to 1
8

What are the foci of the hyperbola whose equation is the fraction with numerator open paren x minus 6 close paren squared and denominator 16 minus the fraction with numerator open paren y plus 7 close paren squared and denominator 9 is equal to 1 ?

A
open paren 6 comma negative 12 close paren and open paren 6 comma negative 2 close paren
B
open paren 1 comma negative 7 close paren and open paren 11 comma negative 7 close paren
C
open paren 2 comma negative 7 close paren and open paren 10 comma negative 7 close paren
D
open paren 6 comma negative 10 close paren and open paren 6 comma negative 4 close paren
9

One focus of a hyperbola is located at open paren negative 6 comma 2 close paren One vertex of the hyperbola is located at open paren negative 4 comma 2 close paren The center is open paren negative 1 comma 2 close paren What is the equation of the hyperbola?

A
the fraction with numerator open paren x minus 2 close paren squared and denominator 16 minus the fraction with numerator open paren y plus 1 close paren squared and denominator 9 is equal to 1
B
the fraction with numerator open paren x plus 1 close paren squared and denominator 16 minus the fraction with numerator open paren y minus 2 close paren squared and denominator 9 is equal to 1
C
the fraction with numerator open paren x minus 2 close paren squared and denominator 9 minus the fraction with numerator open paren y plus 1 close paren squared and denominator 16 is equal to 1
D
the fraction with numerator open paren x plus 1 close paren squared and denominator 9 minus the fraction with numerator open paren y minus 2 close paren squared and denominator 16 is equal to 1
10

Which point is a focus of the hyperbola?

A
open paren 2 comma 8 close paren
B
open paren negative 3 comma negative 4 close paren
C
open paren 2 comma negative 4 close paren
D
open paren negative 11 comma negative 4 close paren

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