2² y² Mikayla is a calculus student and needs to find the points on the ellipse + 81 1296 = 1 that are furthest away from the point (3, 0). First she draws the diagram shown and then thinks she needs to optimize the distance formula between the fixed point and the general point (x, y). Then Mikayla will use the equation of the ellipse as the constraint to write a function in terms of one variable. Finally she will use calculus to solve the problem. (x,y) (3,0) Follow Mikayla's plan to solve the problem! Points on the ellipse that are furthest from (3, 0): places if necessary. You may round to three decimal
2² y² Mikayla is a calculus student and needs to find the points on the ellipse + 81 1296 = 1 that are furthest away from the point (3, 0). First she draws the diagram shown and then thinks she needs to optimize the distance formula between the fixed point and the general point (x, y). Then Mikayla will use the equation of the ellipse as the constraint to write a function in terms of one variable. Finally she will use calculus to solve the problem. (x,y) (3,0) Follow Mikayla's plan to solve the problem! Points on the ellipse that are furthest from (3, 0): places if necessary. You may round to three decimal
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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![Mikayla is a calculus student and needs to find the points on the ellipse
\[
\frac{x^2}{81} + \frac{y^2}{1296} = 1
\]
that are furthest away from the point \((3, 0)\). First, she draws the diagram shown and then thinks she needs to optimize the distance formula between the fixed point and the general point \((x, y)\). Then Mikayla will use the equation of the ellipse as the constraint to write a function in terms of one variable. Finally, she will use calculus to solve the problem.
**Diagram Explanation:**
The diagram shows an ellipse centered at the origin, with its major axis along the y-axis. The equation of the ellipse is given as \(\frac{x^2}{81} + \frac{y^2}{1296} = 1\).
- A general point \((x, y)\) is marked on the ellipse.
- The fixed point \((3, 0)\) lies on the x-axis.
- The distance \(d\) is drawn between the fixed point \((3, 0)\) and the point \((x, y)\) on the ellipse.
**Task:**
Follow Mikayla's plan to solve the problem!
Points on the ellipse that are furthest from \((3, 0)\): [Input box]
You may round to three decimal places if necessary.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b638ef2-9928-44ee-907b-a6bc7b9add08%2Fda8304f1-1561-4864-8ffe-f28cc853fa77%2Fyz6jwin_processed.png&w=3840&q=75)
Transcribed Image Text:Mikayla is a calculus student and needs to find the points on the ellipse
\[
\frac{x^2}{81} + \frac{y^2}{1296} = 1
\]
that are furthest away from the point \((3, 0)\). First, she draws the diagram shown and then thinks she needs to optimize the distance formula between the fixed point and the general point \((x, y)\). Then Mikayla will use the equation of the ellipse as the constraint to write a function in terms of one variable. Finally, she will use calculus to solve the problem.
**Diagram Explanation:**
The diagram shows an ellipse centered at the origin, with its major axis along the y-axis. The equation of the ellipse is given as \(\frac{x^2}{81} + \frac{y^2}{1296} = 1\).
- A general point \((x, y)\) is marked on the ellipse.
- The fixed point \((3, 0)\) lies on the x-axis.
- The distance \(d\) is drawn between the fixed point \((3, 0)\) and the point \((x, y)\) on the ellipse.
**Task:**
Follow Mikayla's plan to solve the problem!
Points on the ellipse that are furthest from \((3, 0)\): [Input box]
You may round to three decimal places if necessary.
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