CPM Homework Help : PC3 Problem 10-85

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10-85.

Graph each equation below. Also include all of the key information, such as the locations of the foci and/or the equations of any asymptotes.

$\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 }= 1$
Hint (a):
Since the terms are both squared, being added, and the equation is equal to $1$ , this is an ellipse.
More Help (a):
The center is at $(1, 0)$ . The 'horizontal radius' = 3 and the 'vertical radius' $= 2$ .

$(x − 4)^2 + (y + 2)^2 = 25$
Hint (b):
This equation has the form $(x − h)^2 + (y − k)^2 = r^2$ , so this is a circle.

$\frac { ( y - 2 ) ^ { 2 } } { 36 } - \frac { ( x - 3 ) ^ { 2 } } { 9 }= 1$
Hint (c):
The terms are both squared, being subtracted, and the $y$ -term is positive.
More Help (c):
This is a hyperbola that is vertically oriented.

$5x + (y − 2)^2 = 20$
Hint (d):
When you isolate the $x$ -term, the equation becomes:
$x=-\frac{1}{5}(y-2)^2+5$
More Help (d):
This is a parabola that opens to the left.

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