Alg_Complete

# 2 2 x 3 y 1 1 solution a 25 49 2 y 2 b

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Unformatted text preview: + a, k ) left most point : ( h - a, k ) top most point : ( h, k + b ) bottom most point : ( h, k - b ) Note that a is the square root of the number under the x term and is the amount that we move right and left from the center. Also, b is the square root of the number under the y term and is the amount that we move up or down from the center. Let’s sketch some graphs. Example 1 Sketch the graph of each of the following ellipses. 2 2 ( x + 2 ) + ( y - 4 ) = 1 [Solution] (a) 9 25 x 2 ( y - 3) (b) + = 1 [Solution] 49 4 2 2 (c) 4 ( x + 1) + ( y + 3) = 1 [Solution] 2 Solution (a) So, the center of this ellipse is ( -2, 4 ) and as usual be careful with signs here! Also, we have a = 3 and b = 5 . So, the points are, right most point : (1, 4 ) left most point : ( -5, 4 ) top most point : ( -2,9 ) bottom most point : ( -2, -1) © 2007 Paul Dawkins 216 http://tutorial.math.lamar.edu/terms.aspx College Algebra Here is a sketch of this ellipse. [Return to Problems] (b) The center for this part is ( 0,3) and we have a = 7 and b = 2 . The points we need are, righ...
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