Flashcards
Transformations of conics
Cards in this deck (13)
- 1Before we transform a conic, what should we do?Get x values and y values both on the same side
- 2How should we go about translating by the vector [a][0] ?Replace x with (x-a)
- 3How should we go about translating by the vector [0][b] ?Replace y with (y-b)
- 4How should we go about stretching in the x-direction by sf a ?Replace x with (x/a)
- 5How should we go about stretching in the y-direction by sf b ?Replace y with (y/b)
- 6How should we go about a reflection in the x-axis ?Replace y with (-y)
- 7How should we go about a reflection in the y-axis ?Replace x with (-x)
- 8How should we go about a reflection in the line y=x ?Replace all y's with x's and all x's with y's
- 9How should we go about a reflection in the line y=-x ?Replace all y's with -x's and all x's with -y's
- 10Translate x^2/6 + y^2/2 = 1 by the vector [3][-2](x-3)^2/6 + 3(y+2)^2/6 = 1
Same as (x-3)^2 + 3(y+2)^2 = 6
Expand for x^2+6x+3y^2+12y+15=0 - 11Stretch y^2=18x in the y-direction sf 3(y/3)^2 = 18x , y^2/9 = 18x , y^2=162x
- 12Reflect x^2/6 - y^2/9 = 1 in line y=xy^2/6 - x^2/9 = 1 , 3y^2/18 - 2x^2/18 = 1
3y^2 - 2x^2 = 18 - 13Reflect y^2=4x in y-axisy^2=-4x , y^2+4x=0