How Can I Find Tangents on a Surface Passing Through an External Point?

[AtulSharma]

Finding Tangents... Interesting !

Hello,

I have an interesting problem for you.

I have a surface & an external point which is outside the surface.

I need to find the equation of all the tangents on this surface which pass through the external point.

Regards,
AtulSharma

 

[sutupidmath]

Hello,

I have an interesting problem for you.

I have a surface & an external point which is outside the surface.

I need to find the equation of all the tangents on this surface which pass through the external point.

Regards,
AtulSharma

Are you just trying to test us, or you really need an answer to this question?

 

[AtulSharma]

I myself need an answer to the problem.

 

[sutupidmath]

well, i am not sure whether my reasoning will be fine, because you have this surface, so if it were a curve it would most likely go like this.
You first find the derivative of that function, most likely you will have to differentiate it implicitly, so this way you will manage to find the slope of the tangent line at any point on that surface, curve. So now you have this external point call it (x_1,y_1), so now the slope of the tangent will be

\frac{y-y_1}{x-x_1}=m, but now you also have the slope of the tangent line at any point dy/dx so

\frac{dy}{dx}=\frac{y-y_1}{x-x_1}, so you will manage to find a relation between x, and \ y but you also have one relation given by the eq of the curve, so i think now you have to look for a solution, when this line only touches that curve. I am not sure whether my reasoning is okay, but wait for other replies as well!

 

[AtulSharma]

Well, I think its a good way to try. Let's see other replies also.

Thanks for this solution.

 

[rcgldr]

Is this a 2D or 3D problem. If it's a 3D problem, are you looking for all the tangent planes that include the outside point, or only tangent lines that go through the point (in this case you end up with a cone)? If it's a 2D problem then you just end up with 2 lines. This is assuming the surface isn't complex, such as one that has both concave and covex components.

 

[AtulSharma]

This is a 3D problem. I need to find some (not all) of the tangents passing through the external point.