MAT224H1 Lecture : Drawing planar quadratic, quadratic forms, orthonormal basis and matricies, gram-schmidt orthogonalization process
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We all know what the equation x2 + y2 = 1 describes: it is the equation of a unit circle: (x, y) It is easy to see what shape is described by the equation x2. If a point (x, y) lies on this shape, then the point (x/3, y/2) lies on the unit circle. So in fact what we have is the result of stretching the unit circle by a factor of 3 in the x direction and by a factor of 2 in y direction. Much harder is to describe how the locus of points (x, y) satisfying 3x2 + In fact we will spend the next two lectures learning. 1 www. notesolution. com how to bring this equation to the much more manageable form. For this equation the coordinates x = x+y 2. = 1 seem to be useful, as in these coordinates the equation has the familiar form 5 x2 + y2 = 1, which describes an ellipse.
