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#1 2006-11-17 09:47:05

Dharshi
Member
Registered: 2006-10-31
Posts: 56

Need help

Find the equation of tangent to the parabola y^2 = 4x +5 which is parallel to the line y = 2x +7

How can we solve this without using differentiation?

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#2 2006-11-17 10:41:32

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Need help

I can't think of any easy way to solve that without differentiation. Not algebraically, that is.

Maybe the question just wants you to draw the parabola and the line and use that to find where the tangent is.

I've cheated and used differentiation to work it out, so I can confirm that the answer works out nicely, with no horrible roots or decimals or anything, so a graphical method would get you an accurate answer.


Why did the vector cross the road?
It wanted to be normal.

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#3 2006-11-17 15:41:32

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Need help

How can we solve this without using differentiation?

In short, you can't.  You can solve it with limits, technically, but thats exactly what differentiation is.  There is a reason why we have differentiation, and it's to solve problems with slope and tangent lines, such as this.

Why do you wish to do this without differentiation?  Is it just because you don't wish to learn how?

I've cheated and used differentiation to work it out, so I can confirm that the answer works out nicely, with no horrible roots or decimals or anything, so a graphical method would get you an accurate answer.

That's just "visual" differentiation.  At least in my opinion.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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