# line that is tangent to a curve ata particular point

• Apr 15th 2012, 10:55 AM
Bowlbase
line that is tangent to a curve ata particular point
Find the line that is tangent to the curve with the function y^2=x+3 at point (6,-3)

I know m=dy/dx so implicit derivative is: 2y dy/dx=1, so dy/dx = 1/2y

then equation of a line y-y_1=m(x-x_1). thus y+3=1/2y(x-6)

I can't believe that this is suppose to be my answer as this is clearly not a straight line. What am I doing wrong?

Thanks
• Apr 15th 2012, 11:02 AM
Plato
Re: line that is tangent to a curve ata particular point
Quote:

Originally Posted by Bowlbase
Find the line that is tangent to the curve with the function y^2=x+3 at point (6,-3)
I know m=dy/dx so implicit derivative is: 2y dy/dx=1, so dy/dx = 1/2y
then equation of a line y-y_1=m(x-x_1). thus y+3=1/2y(x-6)
I can't believe that this is suppose to be my answer as this is clearly not a straight line. What am I doing wrong?

At the point $(6,-3)$ we have $\frac{dy}{dx}=\frac{-1}{6}$.
• Apr 15th 2012, 11:08 AM
Bowlbase
Re: line that is tangent to a curve ata particular point
Really, that simple? Geez..

Thanks
• Apr 15th 2012, 01:32 PM
Bowlbase
Re: line that is tangent to a curve ata particular point
Rather than make a new thread I have similar question as before but no points given

Find all the lines tangent to the curve y=x^3 and is parallel to y=3x-5.

I have that the slope must be the same as the given line, so m=3. The derivative of the curve also gives slope so 3x^2=3 where x is +-1.

So I have only 1 point to find in my line equation. I have y-y_1=3(x+-1). I'm stuck on trying to figure out what y_1 is here.

Pretty sure this is going to be another oh geez moment. Thanks for the help.
• Apr 15th 2012, 01:45 PM
Plato
Re: line that is tangent to a curve ata particular point
Quote:

Originally Posted by Bowlbase
Rather than make a new thread I have similar question as before but no points given
Find all the lines tangent to the curve y=x^3 and is parallel to y=3x-5.
I have that the slope must be the same as the given line, so m=3. The derivative of the curve also gives slope so 3x^2=3 where x is +-1.
So I have only 1 point to find in my line equation. I have y-y_1=3(x+-1). I'm stuck on trying to figure out what y_1 is here.

Always, always start a new thread for a new question!

You have two points of tangency $((1,1)~\&~(-1,-1)$
So you have two tangent lines.
• Apr 15th 2012, 01:58 PM
Bowlbase
Re: line that is tangent to a curve ata particular point
Sorry, I'll make a new thread next time.

So I understand that there will be two lines but I don't see where the y values are coming from. I am assuming that you just put the x values into the y=x^3. Is this correct?
• Apr 15th 2012, 02:23 PM
skeeter
Re: line that is tangent to a curve ata particular point
Quote:

Originally Posted by Bowlbase
So I understand that there will be two lines but I don't see where the y values are coming from. I am assuming that you just put the x values into the y=x^3. Is this correct?

since the tangent line "touches" the curve at the point of tangency, that would be correct.
• Apr 15th 2012, 02:50 PM
Bowlbase
Re: line that is tangent to a curve ata particular point
makes perfect sense, thank you.