Explanation Definition used: Suppose x -and y -axes in a coordinate plane are rotated through an acute angle ϕ to produce the X and Y axes. Then the coordinates x of point in xy -plane in terms of X and Y is given by, x = X cos ϕ − Y sin ϕ And, the coordinate y of a point in xy -plane in terms of X and Y is, y = X sin ϕ + cos ϕ . Calculation: The given equation conic is x 2 + 2 3 x y − y 2 = 4 (1) From the definition stated above, the coordinate x of a point in xy -plane in terms of X and Y is, x = X cos 30 ° − Y sin 30 ° = X ( 3 2 ) − Y ( 1 2 ) Therefore, x = 3 X 2 − Y 2 (2) And, the coordinate y of a point in xy -plane in terms of X and Y is, y = X sin 30 ° + Y cos 30 ° = X ( 1 2 ) + Y ( 3 2 ) y = X 2 + 3 Y 2 (3) Substitute x and y coordinates represented by equations (2) and (3) in (1). Therefore, equation (1) becomes, ( 3 X 2 − Y 2 ) 2 + 2 3 ( 3 X 2 − Y 2 ) ( X 2 + 3 Y 2 ) − ( X 2 + 3 Y 2 ) 2 = 4 1 4 ( 3 X − Y ) 2 + 2 3 2 ( 3 X − Y ) 1 2 ( X + 3 Y ) −<

7th Edition

ISBN: 9781305718906

Author: Stewart

Publisher: CENGAGE L

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Chapter 11.5, Problem 13E

To determine

The equation of conic x2+23xy−y2=4 in XY-coordinates, when the coordinate axes are rotated through ϕ=30° .

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Chapter 11.5, Problem 12E

Chapter 11.5, Problem 14E

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Chapter 11 Solutions

PRECALCULUS: MATHEMATICS FOR CALCULUS

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The equation of conic x 2 + 2 3 x y − y 2 = 4 in XY -coordinates, when the coordinate axes are rotated through ϕ = 30 ° .

Solution Summary: The author explains the equation of conic, which is x2+1sqrt3Xy-y=4 in XY-coordinates, when the coordinate

The equation of conic x2+23xy−y2=4 in XY-coordinates, when the coordinate axes are rotated through ϕ=30° .

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Chapter 11 Solutions