AnswersPrecalculusThe General Equation of Conic Sections

The General Equation of Conic Sections — Quiz Answers

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1
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Which equation represents an ellipse?

A
9 x squared plus 3 x plus 9 y squared minus 2 y plus 5 is equal to 0
B
2 x squared minus 4 x y plus 2 y squared plus x minus 3 y plus 5 is equal to 0
C
3 x squared plus 7 x y plus 8 y squared plus 3 x minus 9 y plus 5 is equal to 0
D
2 x squared minus 6 x y plus y squared plus 8 x minus y plus 2 is equal to 0
2
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The graph of y squared plus 8 y minus 4 x minus 24 is equal to 0 is a parabola. Where is the vertex located?

A
open paren negative 5 comma negative 4 close paren
B
open paren negative 1 comma negative 4 close paren
C
open paren negative 6 comma negative 4 close paren
D
open paren negative 10 comma negative 4 close paren
3

Write the equation y squared plus 6 y minus 12 x minus 39 is equal to 0 in standard form.

A
open paren y plus 3 close paren squared is equal to 12 x plus 39
B
open paren y plus 3 close paren squared is equal to 12 times open paren x plus 4 close paren
C
open paren y plus 9 close paren squared is equal to 12 times open paren x plus 4 close paren
D
open paren y plus 9 close paren squared is equal to 12 x plus 39
4

Convert the equation into standard form. 25 x squared minus 9 y squared plus 200 x plus 18 y plus 166 is equal to 0

A
the fraction with numerator open paren x plus 8 close paren squared and denominator 9 minus the fraction with numerator open paren y minus 2 close paren squared and denominator 25 is equal to 1
B
the fraction with numerator open paren x minus 4 close paren squared and denominator 9 minus the fraction with numerator open paren y plus 1 close paren squared and denominator 25 is equal to 1
C
the fraction with numerator open paren x plus 4 close paren squared and denominator 9 minus the fraction with numerator open paren y minus 1 close paren squared and denominator 25 is equal to 1
D
the fraction with numerator open paren x minus 8 close paren squared and denominator 9 minus the fraction with numerator open paren y plus 2 close paren squared and denominator 25 is equal to 1
5

What is the standard form of the following equation? 4 x squared plus 9 y squared plus 24 x minus 36 y plus 36 is equal to 0

A
the fraction with numerator open paren x plus 3 close paren squared and denominator 4 plus the fraction with numerator open paren y minus 2 close paren squared and denominator 9 is equal to 1
B
the fraction with numerator open paren x plus 3 close paren squared and denominator 4 plus the fraction with numerator open paren y minus 2 close paren squared and denominator 9 is equal to 0
C
the fraction with numerator open paren x plus 3 close paren squared and denominator 9 plus the fraction with numerator open paren y minus 2 close paren squared and denominator 4 is equal to 0
D
the fraction with numerator open paren x plus 3 close paren squared and denominator 9 plus the fraction with numerator open paren y minus 2 close paren squared and denominator 4 is equal to 1
6

Which conic section is represented by the following equation? 3 x squared minus 7 x plus 8 y squared minus 2 y plus 1 is equal to 0

A
circle
B
parabola
C
ellipse
D
hyperbola
7

Graph the fraction with numerator open paren x minus 4 close paren squared and denominator 4 plus the fraction with numerator y squared and denominator 9 is equal to 1

A
Image with description On a coordinate plane, an Ellipse has center point (negative 4, 0) and goes through (negative 1, 0), (negative 4, 2), (negative 7, 0) and (negative 4, negative 2).
B
Image with description On a coordinate plane, an Ellipse has center (negative 4, 0) and goes through (negative 2, 0), (negative 4, 3), (negative 6, 0) and (negative 4, negative 3).
C
Image with description On a coordinate plane, an Ellipse has center point (4, 0) and goes through (4, 2), (7, 0), (4, negative 2), and (1, 0).
D
Image with description On a coordinate plane, an Ellipse has center (4, 0) and goes through (6, 0), (4, negative 3), (2, 0) and (4, 3).
8

Which conic section is represented by the following equation? 9 x squared minus 5 x minus 3 y squared minus 2 y plus 4 is equal to 0

A
hyperbola
B
parabola
C
circle
D
ellipse
9

Which conic section is represented by the following equation? 5 x squared minus x plus 5 y squared minus 3 y minus 12 is equal to 0

A
ellipse
B
parabola
C
circle
D
hyperbola
10

Which equation represents a parabola?

A
negative 3 x plus 4 y squared minus 2 y plus 6 is equal to 0
B
x squared plus x minus 2 y squared minus 4 y plus 2 is equal to 0
C
4 x squared minus 2 x plus 3 y squared minus y plus 1 is equal to 0
D
2 x squared plus y squared minus 4 y plus 6 is equal to 0

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