How do you find the points of an ellipse where the tangent equals 1?

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Homework Help Overview

The discussion revolves around finding points on the ellipse defined by the equation x^2/9 + y^2/16 = 1 where the slope of the tangent line equals 1. Participants explore the relationship between the slope of the tangent and the coordinates of the ellipse.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of implicit differentiation and the need to express y in terms of x before differentiating. There are attempts to solve for points by substituting expressions derived from the slope equation into the ellipse equation.

Discussion Status

The conversation includes various approaches to solving the problem, with some participants questioning the correctness of their algebraic manipulations. There is a mix of suggestions and clarifications regarding the differentiation process and the substitution of variables.

Contextual Notes

Some participants express uncertainty due to gaps in their mathematical background, particularly regarding calculus concepts. The discussion reflects a collaborative effort to clarify these concepts while adhering to homework guidelines.

  • #31
Hahaha uhhh I guess the negative of 3.2, so -3.2 ? Good point. So because it's an ellipse then there are necessarily 2 points where dy/dx = 1 and so my answer should be like (4.5, -3.2) and (-4.5, 3.2) eh?
 
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  • #32
Yes, that is right.
 
  • #33
Hurray! Thanks errbody. You guyz are so smart!
 

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