Question

I was trying to answer this question
http://openstudy.com/study#/updates/4f985725e4b000ae9ecdf837
then suddenly this came to my mind "Can we say that a tangent to parabola intersects with parabola at only one point" if yes can someone prove it

Answer 1

yes

Answer 2

It doesn't "intersect" cause that would involve it passing through one side of the parabola, and then coming out the other end. A tangent merely touches the curve at one point only.

Answer 3

it intersects a point not the parabola

Answer 4

hope that clears it up

Answer 5

You can simply find the slope of the tangent by taking the derivative of the function and making it equal to zero, solving it for x.

Plug in your values for (x, y) at a certain point, combined with the slope you found by differentiating and then you have an equation for the slope which touches the function/parabola.

I don't really know what you're asking, but this is how you prove the tangent exists, although it can only really exist as a mathematical representation, afterall - you can never actually draw a perfect tangent.

Answer 6

yeah, dy/dx is a good method

Answer 7

a medal for you sir

Answer 8

^_^ thank you

Answer 9

But guys I am looking for a general mathematical proof that regardless of what point you chose on parabola the tangent at that point intersects the parabola at only one point.
@chasie I understand what you are saying when b^2 - 4ac = 0 then there will be one point of intersection. but I am looking for general proof regardless of the point that you chose. I tried to prove it myself, and I could not