Precalc0103to0104-page37

Precalc0103to0104-page37 - We want to translate the circle...

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(Section 1.4: Transformations) 1.4.13 PART F: TRANSLATIONS THROUGH COORDINATE SHIFTS Translations through Coordinate Shifts A graph G in the xy -plane is shifted h units horizontally and k units vertically . • If h < 0 , then G is shifted left by h units. • If k < 0 , then G is shifted down by k units. To obtain an equation for the new graph, take an equation for G and: • Replace all occurrences of x with x ± h () , and • Replace all occurrences of y with y ± k () . Example 11 (Translating a Circle through Coordinate Shifts; Revisiting Section 0.13)
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Unformatted text preview: We want to translate the circle in the xy-plane with radius 3 and center 0, 0 ( ) so that its new center is at 2, 1 ( ) . Find the standard form of the equation of the new circle. Solution We take the equation x 2 + y 2 = 9 for the old black circle and: Replace x with x 2 ( ) ( ) , or x + 2 ( ) , and Replace y with y 1 ( ) . This is because we need to shift the black circle left 2 units and up 1 unit to obtain the new red circle....
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