Deck 10: Topics From Analytical Geometry

Question 1

Classify the conic.

A) parabola
B) ellipse
C) circle
D) hyperbola

Answer 1

A

Question 2

Find an equation for the set of points in an xy-plane that are equidistant from the point P and the line l. $P ( - 6,3 ) , l : x = - 2$

A) $( x - 3 ) ^ { 2 } = - 8 ( y + 4 )$
B) $( y - 3 ) ^ { 2 } = - 8 ( y + 4 )$
C) $( y + 3 ) ^ { 2 } = - 8 ( y + 4 )$
D) $( y - 3 ) = - 8 ( y + 4 ) ^ { 2 }$
E) $( y - 3 ) ^ { 2 } = ( y + 4 )$

Answer 2

$( y - 3 ) ^ { 2 } = - 8 ( y + 4 )$

Question 3

Find an equation for the parabola that has a horizontal axis and passes through the given points.

A)
B)
C)
D)
E)

Answer 3

E

Question 4

Find the foci of the ellipse.

A)
B)
C)
D)
E)

Question 5

Find a polar equation in r and that has the same graph as the equation in x and y.

A)
B)
C)
D)
E)

Question 6

Find a parametrization that gives the same graph as the given equation.

A)
B)
C)
D)
E)

Question 7

Find the foci of the ellipse.

A)
B)
C)
D)
E)

Question 8

Lissajous figures are used in the study of electrical circuits to determine the phase difference between a known voltage and an unknown voltage having the same frequency. The voltages are graphed parametrically as and . If is acute, then where y _int is the nonnegative y -intercept and y _max is the maximum y -value on the curve. Graph the parametric curve and use the graph to approximate in degrees if

A)
B)
C)
D)
E)

Question 9

Sketch the graph of the ellipse, showing the foci .

A)
B)
C)
D)

Question 10

Find the eccentricity.

A)
B)
C)
D)
E)

Question 11

Find a polar equation in r and that has the same graph as the equation in x and y.

A)
B)
C)
D)
E)

Question 12

Find an equation for the ellipse shown in the figure.

A)
B)
C)
D)
E)

Question 13

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola.

A) Parabola with vertical axis
B) Hyperbola
C) Ellipse
D) Parabola with horizontal axis
E) Circle

Question 14

Shown in the figure is the Lissajous figure given by Find the period of the figure - that is, the length of the smallest t-interval that traces the curve.

A)
B)
C)
D)
E)

Question 15

Find an equation in x and y for the polar equation.

A)
B)
C)
D)
E)

Question 16

An arch of a bridge is semi-elliptical, with major axis horizontal. The base of the arch is 30 feet across, and the highest part of the arch is 10 feet above the horizontal roadway, as shown in the figure. Find the height of the arch 7 feet from the center of the base.

A) 12.1 ft
B) 8.8 ft
C) 17.7 ft
D) 11.0 ft
E) 7.3 ft

Question 17

Find an equation of the parabola that satisfies the condition. Vertex $V ( - 4,0 )$ , focus $F ( - 2,0 )$

A) $y = 8 ( x + 4 ) ^ { 2 }$
B) $y ^ { 2 } = 8 ( x - 4 )$
C) $y ^ { 2 } = 8 ( x + 4 )$
D) $y ^ { 2 } = ( x + 4 )$
E) $x ^ { 2 } = 8 ( y + 4 )$

Question 18

Sketch the graph of the polar equation

A)
B)
C)
D)

Question 19

Find a polar equation in r and that has the same graph as the equation in x and y.

A)
B)
C)
D)
E)

Question 20

Find an equation for the ellipse that has its center at the origin and satisfies the conditions.

A)
B)
C)
D)
E)

Question 21

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

A)
B)
C)
D)
E)

Question 22

Find a polar equation in r and of the parabola with focus at the pole and the given vertex.

A)
B)
C)
D)
E)

Question 23

Find a polar equation in r and of the parabola with focus at the pole and the given vertex.

A)
B)
C)
D)
E)

Question 24

Polar equations of conics can be used to describe the motion of comets. These paths can be graphed using the following polar equation, where e is the eccentricity of the conic and r _per is the perihelion distance measured in AU. For Encke's Comet r _per = 0.3317 and e = 0.8499, determine whether its trajectory is elliptical, parabolic, or hyperbolic.

A) parabolic
B) elliptical
C) hyperbolic

Question 25

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

A)
B)
C)
D)
E)