Finding equation of both lines

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Homework Help Overview

The problem involves finding the equations of the lines that are tangent to the curve defined by y=x^2 + 4 and that also pass through the point (1, -2).

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to determine the slope of the tangent using the derivative, which is noted as 2x. Some participants suggest finding the slope of the line connecting a point on the curve to the point (1, -2) and equating it to the derivative. There are questions about the next steps after finding x and the correct formulation of the slope.

Discussion Status

Participants are exploring different interpretations of the problem and discussing the relationships between the slopes and points involved. There is an ongoing dialogue about how to proceed after determining the value of x, indicating a productive exchange of ideas without a clear consensus yet.

Contextual Notes

There is a focus on ensuring the slopes are correctly calculated and applied, with some uncertainty about the definitions and relationships involved in the problem setup.

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Homework Statement



Determine the equation of both lines that are tangent to the graph of y=x^2 +4 and pass through the point (1,-2)

Homework Equations





The Attempt at a Solution



The derivative/slope of the tangent is 2x. But I'm not too sure what to do with this.
 
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Ok so let (x,y) be a point on your curve. That makes it (x,x^2+4), right? Now find the slope of the line between that point and (1,-2). That slope should be your 2x, also right? Now solve for x.
 
Dick said:
Ok so let (x,y) be a point on your curve. That makes it (x,x^2+4), right? Now find the slope of the line between that point and (1,-2). That slope should be your 2x, also right? Now solve for x.

Alright. Once I find x, what do I do with it?.

Btw, the slope for that line is (x-1)/(x^2+6) rite?
 
Meeker said:
Alright. Once I find x, what do I do with it?.

Btw, the slope for that line is (x-1)/(x^2+6) rite?

Slope is delta(y)/delta(x), isn't it? Once you find values for x, each one gives you a point on the curve that also goes through (1,-2). Use the points to find the line equations.
 

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