Question

Eliminate the parameter.
x=t^2+2, y=t^2-4

a. y = x - 6, x ≥ 1

b. y = x + 6, x ≥ 1

c. y = x2 - 6, x ≥ 1

d. y = x2 + 6, x ≥ 1

Answer 1

we need to eliminate t^2, right ?

so can you isolate t^2 from
\( x= t^2+2 \)??

Answer 2

hint :
subtract 2 from both sides :)

Answer 3

x-2=t^2

Answer 4

yes!
now plug that t^2 in

y= t^2 -4

Answer 5

y = (x-2) -4
simplify :)

Answer 6

y=-4x+8

Answer 7

not actually

y = x-2 -4 is just
y= x-6

Answer 8

option A :)

Answer 9

Oh yeah!

Answer 10

:)

Answer 11

Can you help me with one more please?

Answer 12

for sure :)

Answer 13

Eliminate the parameter.

x = 3 cos t, y = 3 sin t

Answer 14

square and add


1) x= 3 cos t
Square both sides

2)
y= 3 sin t
square both sides

what do u get ?

Answer 15

x^2=3 cos^2 t
y^2=3 sin^2 t

Answer 16

now add these equations!

Answer 17

How?

Answer 18

\(\Large x^2+y^2 =3 cos^2 t
+3 sin^2 t
\)

can you simplify this ?

Answer 19

I have no idea what to do

Answer 20

factor out the 3 from the right!

Answer 21

and then use
\(\large \sin^2x +\cos^2 x =1 \)

Answer 22

So where would I have the 3?

Answer 23

\(x^2 + y^2 = 3 (\sin^2x +\cos^2 x ) = 3 \times 1 \\ \Large x^2+y^2 = 3 \)

thats it!

Answer 24

Oh! Thank you so much!! :)

Answer 25

most welcome ^_^