Describe one similarity and one difference between the graphs of x225+y216=1and(x−1)225+(y−1)216=1.

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odgovoreh · Accepted Answer

Step 1  Consider the following equations of two ellipses, x225+y216=1and(x−1)225+(y−1)216=1  Step 2  In the given equations x225+y216=1and(x−1)225+(y−1)216=1, he denominator of the x2 term is greater than the denominator of the y2-term, so the major axis horizontal and parallel to x-aixs.  Compare the first equation x225+y216=1 with the standard form (x−h)2a2+(y−k)2b2=1.  It is observed that a2=25,b2=16,h=0andk=0.  That is, a = 5, b = 4, h = 0 and k = 0.  The center of the ellipse x225+y216=1 is at origin, major axis is along x-axis and minor axis is along y-axis.  Compare the second equation (x−1)225+(y−1)216=1 with the standard form  (x−h)2a2+(y−k)2b2=1  It is observed that a2=25,b2=16, h = 1 and k = 1.  That is, a = 5, b = 4, h = 1 and k = 1.  The center of the ellipse (x−1)225+(y−1)216=1 is at point (1,1), major axis is along x-axis and minor axis is along y-axis.  Similarity is the major axis of two graphs is horizontal and of same length. Difference is center of ellipse   x225+y216=1 is at (0,0) and center of ellipse (x−1)225+(y−1)216=1 is at point (1,1).

Describe one similarity and one difference between the graphs of x2/25 + y2/16 = 1 and (x - 1)2/25 + (y - 1)2/16 = 1.

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