Let E be the ellipse given by the equation x^2 + 5y^2= 6, If m is any real number, and all tangent lines to E that pass through the point
(m; 0).

Question

Let E be the ellipse given by the equation x^2 + 5y^2= 6, If m is any real number, and all tangent lines to E that pass through the point
(m; 0).

anonymous · Answer

it should say....(find all the tangent lines thorugh the point (m,0))

anonymous · Answer

When it says the point (m,0), by m does it mean the slope? 
Assuming it does, I took the derivative of the equation giving me (-x/5y) which is the slope. 
How do I find the actual point for "x" though?

anonymous · Answer

i assume m is the x value but i dont no....thats why im so confused

anonymous · Answer

Same here. How many tangent lines are there? Just one?

anonymous · Answer

thats the question....it wants to know how many there are....an educated guess is 4

anonymous · Answer

Yeah thats what I thought too. I just don't really know how to get any of the other ones. It only gives one point.

anonymous · Answer

my problem is, if were assuming m=x and y=0 then if u put in the 0 the slope you get a 0 in the denominator making the slope undefined

anonymous · Answer

That's my problem too. There is the other way of doing the derivative that gives you 5y/-x but even still that will give you x=0. So the point would be (0,0) which is totally incorrect.

anonymous · Answer

i know...im so frustrated lol. i put 0 in for y in the original equation to get x=sqrt of 6....idk how that helps tho

anonymous · Answer

So the point would be (sqrt(6),0) which I mean could make sense. But how would you go about finding the other Tangent lines. 
I wish someone who knew this stuff would give some input.

anonymous · Answer

actually. if you can find the slope of the radius then you can take the opposite reciprocal and get the tangent line since the radius and tangent line are perpendicular

anonymous · Answer

How would you go about doing that? 
It doesnt show any sort of length for the ellipse.

anonymous · Answer

idk....but actually an ellipse technically has no radius but has foci...i think its something like what i proposed above but i really dont know how to do it

anonymous · Answer

Ah okay. I'll probably go hit up the lab in the morning before class and try to figure it out. I don't really know what else I can do.