How do I solve 14? Sure! Here is the transcription of the image content with detailed explanation for an educational context: ---### Section 10.6: Plane Curves and Parametric Equations#### Objective 2: Eliminate the Parameter**For Exercises 11–26,**a. **Eliminate the parameter and write an equation in rectangular coordinates.**b. **Sketch the curve and indicate its orientation.** \[(See Examples 2–3)\]**Exercises:**11. $ x = t + 2 $ and $ y = t^2 + t $12. $ x = t - 1 $ and $ y = t^2 - 2t $13. $ x = t - 1 $ and $ y = \frac{t}{t - 1} $14. $ x = t + 2 $ and $ y = \frac{t}{t + 2} $15. $ x = |t + 3| $ and $ y = 1 + t $16. $ x = |t - 3| $ and $ y = t - 2 $17. $ x = e^t $ and $ y = e^t $18. $ x = 2e^t $ and $ y = e^t - 2 $19. $ x = \sqrt{t} $ and $ y = \sqrt{16 - t} $20. $ x = -\sqrt{9 - t} $ and $ y = \sqrt{t} $21. $ x = \cos t $ and $ y = \sin^2 t - 4 $22. $ x = -\sin t $ and $ y = 1 + \cos^2 t $*(Hint for 21 and 22: Use the identity $ \sin^2 t + \cos^2 t = 1 $)*23. $ x = 5 \cos \theta $ and $ y = 5 \sin \theta $24. $ x = 4 \sin \theta $ and $ y = -4 \cos \theta $25. $ x = 1 + 2 \cos \theta $ and $ y = -2 + 3 \sin \theta $26. \(

Given equations - x = t+2t = x-2 ...................(1)Andy = tt+2y = x-2x-2+2…

Answered: : Eliminate the Parameter 1-26,

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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How do I solve 14?

Sure! Here is the transcription of the image content with detailed explanation for an educational context:

---

### Section 10.6: Plane Curves and Parametric Equations

#### Objective 2: Eliminate the Parameter

**For Exercises 11–26,**

a. **Eliminate the parameter and write an equation in rectangular coordinates.**

b. **Sketch the curve and indicate its orientation.** \[(See Examples 2–3)\]

**Exercises:**

11. $ x = t + 2 $ and $ y = t^2 + t $

12. $ x = t - 1 $ and $ y = t^2 - 2t $

13. $ x = t - 1 $ and $ y = \frac{t}{t - 1} $

14. $ x = t + 2 $ and $ y = \frac{t}{t + 2} $

15. $ x = |t + 3| $ and $ y = 1 + t $

16. $ x = |t - 3| $ and $ y = t - 2 $

17. $ x = e^t $ and $ y = e^t $

18. $ x = 2e^t $ and $ y = e^t - 2 $

19. $ x = \sqrt{t} $ and $ y = \sqrt{16 - t} $

20. $ x = -\sqrt{9 - t} $ and $ y = \sqrt{t} $

21. $ x = \cos t $ and $ y = \sin^2 t - 4 $

22. $ x = -\sin t $ and $ y = 1 + \cos^2 t $

*(Hint for 21 and 22: Use the identity $ \sin^2 t + \cos^2 t = 1 $)*

23. $ x = 5 \cos \theta $ and $ y = 5 \sin \theta $

24. $ x = 4 \sin \theta $ and $ y = -4 \cos \theta $

25. $ x = 1 + 2 \cos \theta $ and $ y = -2 + 3 \sin \theta $

26. \(

Expert Solution

Step 1

$G i v e n e q u a t i o n s - x = t + 2 t = x - 2 . . . . . . . . . . . . . . . . . . . (1) A n d y = \frac{t}{t + 2} y = \frac{x - 2}{x - 2 + 2} (u \sin g e q u a t i o n (1)) y = \frac{x - 2}{x} . . . . . . . . . . . . . (2) F o r t h i s f u n c t i o n t o b e d e f i n e d, d e n o m i n a t o r c a n n e v e r b e z e r o h e n c e x i s t h e d e n o m i n a t o r A n d, x c a n n e v e r b e 0 S o w e c a n n o t d r a w g r a p h a t x = 0$

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