Question

eliminate the parameter to find a Cartesian equation of the curve.

Answer 1

x= 1/2 cos theta
y= 2 sin theta

0 </ theta </ pi

Answer 2

@triciaal

Answer 3

@Kainui

Answer 4

@triciaal

Answer 5

```
x= 1/2 cos theta
y= 2 sin theta
```

2x^2 = ?
(y/2)^2 = ?

Add them.

Answer 6

wait what how u get that lol

Answer 7

They are given to you in the question

Answer 8

oh riightt... but how would i add them if they have differnt variables

Answer 9

Before adding, have you computed 2x^2 ?

Answer 10

2x^2 = 4x^2?

(y/2 )^2 = y^2 / 4

Answer 11

@fourier

Answer 12

Let's try again

We're given
```
x= 1/2 cos theta
```

From that,
2x = ?

Answer 13

cos theta ?

Answer 14

Right.

If 2x = cos theta,

then (2x)^2 = ?

Answer 15

cos^2 theta ? since we are squaring

Answer 16

Yes, save that and look at `y`

Answer 17

that would be sin^2 theta

Answer 18

Yes, next add them :

(2x)^2 + (y/2)^2 = ?

Answer 19

hmmm what you mean by adding them ? lol

Answer 20

You have so far

```
(2x)^2 = cos^2theta
(y/2)^2 = sin^2theta
```

Answer 21

(2x)^2 + (y/2)^2 = cos^2 theta + sin^2theta

Answer 22

Adding those two equations gives you


```
(2x)^2 = cos^2theta
(y/2)^2 = sin^2theta
------------------------------
(2x)^2 + (y/2)^2 = ?
```

Answer 23

= 1?

Answer 24

You have it! Does the expression cos^2 + sin^2 ring a bell ?

Answer 25

yes that trig identity but how did my teacher get + / - 1/2 and +/- 2 ?

Answer 26

After eliminating the parameter you have
(2x)^2 + (y/2)^2 = 1

Answer 27

You can simplify that if you want to

Answer 28

4x^2 + y^2 / 4 = 1

Answer 29

You may multiply 4 through out as nobody likes fractions..

Answer 30

can you show me that step

Answer 31

May be leave it like that. What kind of curve is it ?

Answer 32

4x^2 + y^2 / 4 = 1 can be rearranged as

\[\dfrac{x^2}{(1/2)^2} + \dfrac{y^2}{2^2}=1\]

Looks like an ellipse ?

Answer 33

okay so how did you (1/2)^2 on the bototm ?

Answer 34

Would you agree that \(4x^2\) is same as \(\dfrac{x^2}{1/4}\) ?

Answer 35

hmm i think so but how would you know rigth away ? is there like doing the reciprocal

Answer 36

You get to know these by practicing a lot of problems. Don't worry about them for the time being. Just see that they are equivalent..

Answer 37

oh okay hmm so taking x^2 / ( 1/4 ) since its done by the reciprocal?