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In this problem, we want to sketch the graph of the given function, 25x squared plus 9 y squared plus 150x minus 18y plus 9 is equal to 0.
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This question is testing our ability to recognize conic sections, as well as our ability to graph conic sections using transformations of graphs.
00:21
To solve what we need to do is identify the form of our equation as either a conic, a hyperbola, parabola, or ellips given the left, or a limiting form, align, empty, circle, or point given on the right.
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To do so, we need to rewrite our equation using completion of the square to recognize the correct form.
00:37
So completing the square, we add 25 times 9 and 9 times 1 to both sides.
00:44
Thus, we have the equation equals 234...