Use a graphing utility to sketch the intersecting graphs of the equations and determine whether or not the equations are orthogonal. [Two graphs are orthogonal if at their point(s) of intersection their tangent lines are perpendicular to each other.] 2x2+y2 6 y²4x y 2 y 2 43-2 -10 1 2 4-3-2-1 -1 -2 -2 -3 O ** 0 2 34 14 432-10 1 - -2 O The two equations. -Select- orthogonal. A
Use a graphing utility to sketch the intersecting graphs of the equations and determine whether or not the equations are orthogonal. [Two graphs are orthogonal if at their point(s) of intersection their tangent lines are perpendicular to each other.] 2x2+y2 6 y²4x y 2 y 2 43-2 -10 1 2 4-3-2-1 -1 -2 -2 -3 O ** 0 2 34 14 432-10 1 - -2 O The two equations. -Select- orthogonal. A
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Orthogonal Graphs of Equations
**Objective:**
Use a graphing utility to sketch the intersecting graphs of the following equations and determine whether or not the equations are orthogonal.
**Equations:**
\[2x^2 + y^2 = 6\]
\[y^2 = 4x\]
**Definition:**
Two graphs are orthogonal if at their point(s) of intersection, the tangent lines are perpendicular to each other.
**Graph Description:**
There are four graphs depicted, each containing two curves. In each graph, one curve is an ellipse represented by the equation \(2x^2 + y^2 = 6\) and the other curve is a parabola represented by the equation \(y^2 = 4x\). The focus is on where these curves intersect.
1. **First Graph:**
- Shows curves intersecting at the origin and another point.
- Intersection appears to form right angles.
- Consider this for orthogonality.
2. **Second Graph:**
- Displays curves intersecting.
- The intersection does not form right angles.
- This is likely not orthogonal.
3. **Third Graph:**
- Shows curves intersecting again.
- The intersection likely forms right angles indicating orthogonality.
4. **Fourth Graph:**
- Displays curves intersecting at the origin and another point.
- Intersection does not form right angles.
- This is likely not orthogonal.
**Selection Prompt:**
A dropdown menu option exists where you select whether the two equations are orthogonal based on the graphs.
**Conclusion:**
The two equations \(2x^2 + y^2 = 6\) and \(y^2 = 4x\) are likely orthogonal based on the graphs that show intersections forming right angles.
>Select from the options:
The two equations **[Select: are/are not]** orthogonal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0711daf6-3b19-448b-99c0-3e7fe08f4fe3%2Fbfcbd21c-e236-46e5-80be-cad939f99d62%2Fo3l0xsc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Orthogonal Graphs of Equations
**Objective:**
Use a graphing utility to sketch the intersecting graphs of the following equations and determine whether or not the equations are orthogonal.
**Equations:**
\[2x^2 + y^2 = 6\]
\[y^2 = 4x\]
**Definition:**
Two graphs are orthogonal if at their point(s) of intersection, the tangent lines are perpendicular to each other.
**Graph Description:**
There are four graphs depicted, each containing two curves. In each graph, one curve is an ellipse represented by the equation \(2x^2 + y^2 = 6\) and the other curve is a parabola represented by the equation \(y^2 = 4x\). The focus is on where these curves intersect.
1. **First Graph:**
- Shows curves intersecting at the origin and another point.
- Intersection appears to form right angles.
- Consider this for orthogonality.
2. **Second Graph:**
- Displays curves intersecting.
- The intersection does not form right angles.
- This is likely not orthogonal.
3. **Third Graph:**
- Shows curves intersecting again.
- The intersection likely forms right angles indicating orthogonality.
4. **Fourth Graph:**
- Displays curves intersecting at the origin and another point.
- Intersection does not form right angles.
- This is likely not orthogonal.
**Selection Prompt:**
A dropdown menu option exists where you select whether the two equations are orthogonal based on the graphs.
**Conclusion:**
The two equations \(2x^2 + y^2 = 6\) and \(y^2 = 4x\) are likely orthogonal based on the graphs that show intersections forming right angles.
>Select from the options:
The two equations **[Select: are/are not]** orthogonal.
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