The equations of two conics are given below. Choose the correct classification for each, and then provide the requested Information. (a) 2x². 2x + 12xy + 19 = 0 (Choose one) ▼ X ? (b) -9x² + y² + +18x - 4y - 14 = 0 (Choose one) ▼
The equations of two conics are given below. Choose the correct classification for each, and then provide the requested Information. (a) 2x². 2x + 12xy + 19 = 0 (Choose one) ▼ X ? (b) -9x² + y² + +18x - 4y - 14 = 0 (Choose one) ▼
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Conic Sections - Classification and Analysis
The equations of two conics are given below. Choose the correct classification for each, and then provide the requested information.
#### Conic 1:
\[ \text{(a)} \quad 2x^2 + 12x - y + 19 = 0 \]
*Classification Options:* (Dropdown Menu)
- [ ] Circle
- [ ] Ellipse
- [ ] Parabola
- [ ] Hyperbola
#### Conic 2:
\[ \text{(b)} \quad -9x^2 + y^2 + 18x - 4y - 14 = 0 \]
*Classification Options:* (Dropdown Menu)
- [ ] Circle
- [ ] Ellipse
- [ ] Parabola
- [ ] Hyperbola
#### Interactive Tools:
- **Solve Button:** (x)
- **Reset Button:** (⟳)
- **Hint Button:** (?)
---
### Instructions:
1. Carefully analyze each conic equation to determine its type.
2. Use the dropdown menus next to each equation to classify the conic.
3. After selecting the classifications, you may use the interactive tools:
- **Solve Button (x):** Click to solve the conic equations and verify your classification.
- **Reset Button (⟳):** Click to reset your selections.
- **Hint Button (?):** Click to get a hint on how to classify the conics.
### Explanation of Conics:
Conics (or conic sections) are the curves obtained by intersecting a plane with a double-napped cone. There are four types of conic sections:
1. **Circle:** All points at a fixed distance (radius) from a given point (center).
2. **Ellipse:** All points such that the sum of their distances from two fixed points (foci) is constant.
3. **Parabola:** All points equidistant from a given point (focus) and a given line (directrix).
4. **Hyperbola:** All points such that the difference of their distances from two fixed points (foci) is constant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d7590ab-1e8b-4f01-9940-34be16d61a30%2Fdb29186b-3a09-4f93-b874-a41bca025783%2Fhedf8wcs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Conic Sections - Classification and Analysis
The equations of two conics are given below. Choose the correct classification for each, and then provide the requested information.
#### Conic 1:
\[ \text{(a)} \quad 2x^2 + 12x - y + 19 = 0 \]
*Classification Options:* (Dropdown Menu)
- [ ] Circle
- [ ] Ellipse
- [ ] Parabola
- [ ] Hyperbola
#### Conic 2:
\[ \text{(b)} \quad -9x^2 + y^2 + 18x - 4y - 14 = 0 \]
*Classification Options:* (Dropdown Menu)
- [ ] Circle
- [ ] Ellipse
- [ ] Parabola
- [ ] Hyperbola
#### Interactive Tools:
- **Solve Button:** (x)
- **Reset Button:** (⟳)
- **Hint Button:** (?)
---
### Instructions:
1. Carefully analyze each conic equation to determine its type.
2. Use the dropdown menus next to each equation to classify the conic.
3. After selecting the classifications, you may use the interactive tools:
- **Solve Button (x):** Click to solve the conic equations and verify your classification.
- **Reset Button (⟳):** Click to reset your selections.
- **Hint Button (?):** Click to get a hint on how to classify the conics.
### Explanation of Conics:
Conics (or conic sections) are the curves obtained by intersecting a plane with a double-napped cone. There are four types of conic sections:
1. **Circle:** All points at a fixed distance (radius) from a given point (center).
2. **Ellipse:** All points such that the sum of their distances from two fixed points (foci) is constant.
3. **Parabola:** All points equidistant from a given point (focus) and a given line (directrix).
4. **Hyperbola:** All points such that the difference of their distances from two fixed points (foci) is constant.
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