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Draw the Graphs for Three Equations and Find a Common Point

Using first two equations determine 3 possible points that the 2 conic sections that you get from equations meet. Add a third equation figure to out the one point that all three conic sections meet.

First equation is 9(x-squared)+25(y-squared)-72x=81
Second equation is 9(x-squared)-15(y-squared)=9

Graph these two conical sections and let us know how you get the graphs with such things as vertex and foci. Show three common points of these two conical sections. Then add the third equation:12x+6y=-12 and determine one point that all three conical sections share. Please go in to the basics of how to make these graphs from the equations.

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From equation (1): , we get , then we have . Thus it is an ellipse with ...

Solution Summary

Three graphs are drawn and their common point is found. Details are given as to how to how the draw the graphs and how to find vertices, foci and directrices. The drawing of the graph with all three equations is shown.