Equation of Tangent Line for Curve at (5,-3)

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Homework Help Overview

The discussion revolves around finding the equation of the tangent line to a curve defined by the equation \((x-2)^2 + (y+3)^2 = 9\) at the point (5, -3). The subject area includes calculus, specifically the concept of derivatives and tangent lines.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to find the derivative to determine the slope of the tangent line but encounters an undefined slope when substituting the point (5, -3). Some participants question the implications of an undefined slope and explore the nature of the curve as a circle.

Discussion Status

Participants are actively discussing the implications of the undefined slope, with some suggesting that it indicates a vertical tangent line. There is a mix of interpretations regarding the equation of the tangent line, and clarification about the nature of the curve is being explored.

Contextual Notes

There is a mention of the curve being a circle with a specific center and radius, which may influence the understanding of the tangent line's characteristics. Some participants express confusion about the relationship between the circle's properties and the tangent line's equation.

koolkris623
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Find the equation of the line tangent to the curve at (5, -3)
(x-2)^2 + (y+3)^2 = 9

I solved the derivative to be dy/dx = ((-2x+4)/ (2y+6))

when i plugged in the points (5, -3) I got the slope as -6/0...How is this possible??
How can i find the equation of this curve if the slope is undefined??
 
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If the gradient is undefined then, the tangent is vertical line e.g.x=1

btw: that curve, represents a circle with radius 3 and centre (2,-3) so if you are still confused about it, just make a sketch and see
 
Last edited:
wait if its a circle then why isn't the equation x = 5?
 
The equation is x=5, I just used x=1 as an example of what the equation of a line with an undefined gradient looks like
 

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