Parametric equations Flashcards
what a re parametric equations
two equations that seperately define the x and y coordinates of a graph in terms of a third variable
what is a parameter
the third variable of a parametric equation
x = t2+t, y=1-t translated by (3, -1)
stretched by s.f 2 in x dirction
x= t2+t+3, y=-t
x= 2(t2+t), y=1-t
a translation (a, b)
add a to x function
add b to y function
a stretch in x direction
multiply x function
a stretch in y direction
multiply y function
reflect in y axis
multiply x function by -1
reflect in x axis
multiply y function by -1
find coordinates where x=t3+4, y=t2-t meets y=12
12=t2-t
t2-t-12=0
(t-4)(t+3)=0
t= 4 or -3
t=4, x=68
t=13, x-23
(68, 12) and (-23, 12)
to convert parametric equations to ax+by+c
do for x=3t+4, y=2t
make t th subject of one then place that in the other
t=y/2
x=3(y/2) +4
2x-3y-8=0
cartesian equation
x’s and y’s in the same equation.
ax + by +c
x=t3, y =sqrrt(t)
y2=t
x=(y2)3
x=y6
cartesian for
x=t+5, y=t3-t
t=x-5
y=(x-5)3-(x-5)
y=x3-15x2+74x-120
cartesian for x=3t2-4, y=8-t2
t2=8-y
x=3(8-y)-4
x=20-3y
cartesian for x= /t+1, y=t/t-3
x(t+1)=t
tx+x=t
tx-1=-x
t(x-1)=-x
t=-x/x-1
one for t-3 needed
t-x=(-x/x-1) -3
t-3= (-x/x-1) -3(x-1)/x-1
t-3=(-x-3x+3)/x-1
t-3=3-4x/x-1
t/t-3 —-> -x/x-1 x x-11/3-4x = -x(x-1)/(x-1)(3-4x)
=-x/3-4x
