Question 1

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

Accepted Answer

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

Question 2

Find a parametrization that gives the same graph as the given equation. $$y = \ln x ^ { 5 }$$

Accepted Answer

A)  $x = t ^ { 3 } , y = t ^ { 15 }$ 
B)  $x = e ^ { t } , y = \frac { t } { 5 }$ 
C)  $x = \frac { t } { 5 } , y = e ^ { t }$ 
D)  $x = t ^ { 15 } , y = t ^ { 3 }$ 
E)  $x = e ^ { t } , y = 5 t$ 
A)  $x = t ^ { 3 } , y = t ^ { 15 }$ 
B)  $x = e ^ { t } , y = \frac { t } { 5 }$ 
C)  $x = \frac { t } { 5 } , y = e ^ { t }$ 
D)  $x = t ^ { 15 } , y = t ^ { 3 }$ 
E)  $x = e ^ { t } , y = 5 t$

Question 3

Sketch the graph of the polar equation $r = \frac { 40 } { 4 + 10 \cos \theta }$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 4

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola. $$\frac { 1 } { 3 } ( x + 3 ) = y ^ { 2 }$$

Accepted Answer

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

Question 5

Find an equation for the ellipse shown in the figure.

Accepted Answer

A)  $\frac { ( x - 1 ) ^ { 2 } } { 25 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 1 ) ^ { 2 } } { 25 } = 1$ 
C)  $\frac { ( x - 1 ) ^ { 2 } } { 4 } + \frac { ( y + 1 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x + 1 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$ 
E)  $\frac { ( x - 1 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$ 
A)  $\frac { ( x - 1 ) ^ { 2 } } { 25 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 1 ) ^ { 2 } } { 25 } = 1$ 
C)  $\frac { ( x - 1 ) ^ { 2 } } { 4 } + \frac { ( y + 1 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x + 1 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$ 
E)  $\frac { ( x - 1 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$

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

Find a parametrization that gives the same graph as the given equation. $y = \ln x ^ { 5 }$

Sketch the graph of the polar equation $r = \frac { 40 } { 4 + 10 \cos \theta }$

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola. $\frac { 1 } { 3 } ( x + 3 ) = y ^ { 2 }$

Find an equation for the ellipse shown in the figure.

Topics From Algebra

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series, and Probability

Filters

Exam 10: Topics From Analytical Geometry

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=−2P ( - 6,3 ) , l : x = - 2P(−6,3),l:x=−2

Find a parametrization that gives the same graph as the given equation. y=ln⁡x5y = \ln x ^ { 5 }y=lnx5

Sketch the graph of the polar equation r=404+10cos⁡θr = \frac { 40 } { 4 + 10 \cos \theta }r=4+10cosθ40​

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola. 13(x+3)=y2\frac { 1 } { 3 } ( x + 3 ) = y ^ { 2 }31​(x+3)=y2

Find an equation for the ellipse shown in the figure.

Topics From Algebra

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series, and Probability

Filters

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

Find a parametrization that gives the same graph as the given equation. $y = \ln x ^ { 5 }$

Sketch the graph of the polar equation $r = \frac { 40 } { 4 + 10 \cos \theta }$

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola. $\frac { 1 } { 3 } ( x + 3 ) = y ^ { 2 }$