Finding equation of both lines

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In summary, to determine the equation of both lines that are tangent to the graph of y=x^2 +4 and pass through the point (1,-2), first find the slope of the tangent line using the derivative 2x. Then, use this slope to find the value of x by setting it equal to the slope of the line between the point (x,x^2+4) and (1,-2). Once you have the value of x, use it to find the equation of the tangent line by plugging it in as the x-coordinate of a point on the curve and using the point-slope form of a line. Repeat this process for the other tangent line.
  • #1
Meeker
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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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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 

FAQ: Finding equation of both lines

What is the process for finding the equation of two intersecting lines?

The process for finding the equation of two intersecting lines involves identifying the slope and y-intercept of each line, setting the equations equal to each other, and solving for the point where they intersect.

How do you find the slope of a line?

The slope of a line can be found by taking the change in y coordinates over the change in x coordinates, also known as rise over run. This can be calculated by using the formula (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are two points on the line.

What is the formula for finding the y-intercept of a line?

The formula for finding the y-intercept of a line is y = mx + b, where m is the slope and b is the y-intercept. The y-intercept is the point where the line crosses the y-axis.

Can two lines with the same slope intersect?

No, two lines with the same slope will never intersect. This is because parallel lines have the same slope and will never cross each other.

What is the difference between a linear and non-linear equation?

A linear equation is a straight line with a constant slope, while a non-linear equation does not have a constant slope and can have a curved or non-linear shape.

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