Using an Ellipse Consider the region R in the xy-plane bounded by the ellipse
(a) Sketch the graph of the region R and its image S under the given transformation.
(b) Find
(c) Find the area of the ellipse using the indicated change of variables.
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Calculus: Early Transcendental Functions
- G-CO.A.2 Represent and describe transformations in the plane as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. 6) What is the translation image of (5, -3) under the translation (x, y) → (x - 6, y + 2)? 7) a. Find the coordinates of A' if AABC is reflected across the x-axis. C (1, 4) b. If AABC is reflected over the x-axis, what would be the length of A'B'? (0,--2) (4, -2)arrow_forwardPLOT THE IMAGE PRE-IMAGE Transformation COORDINATES c) Pre-Image Points Image Points A'L. A (1,-4) B (2,-1) C (6,-4) B'U. CLJ Isometry? Yes or No Transformation Type: Coordinate Rule (x,y) (y, -x)arrow_forwardWhat does x = 4 represent in xy-plane? Sketch this 2D representation. What does x = 4 represent in space? Carefully sketch this 3-D representation.arrow_forward
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- Convert from rectangular to polar coordinates: Note: Choose r and 0 such that r is nonnegative and 0 < 0 < 2n (a) (8,0) (r,0) (b) (18, ) =(r,0) (c) (-3,3) = (r,0) (d) (-/3,1) →(r,0)arrow_forwardClassIfy and Sketch the surface X2+ Zy² +7? -4x+4y-2z+3•0arrow_forwardclassify and sketch the surface given by x2+2y2+z2-4x+4y-2z+3=0 (indicate the vertex coordinate)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage