# Conc Sectons

1. Jan 16, 2008

### Firepanda

Sorry title was supposed to be Conic Sections, but my I key is sticky :)

I had a queston today, It went somethng like this:

An epllipse of equation ((x^2)/4) + y^2 = 1

Find the equation of the tangent which passes through point P: (4,0)

Well this was a mock exam question, where no answers were available. I keep stumbing on questions of this format and I can never do them.

There is bound to be a routine to go through when caculating something like this and it would be great to know it.

So far I have differentiate implicitly to get dy/dx = -x/4y, point P isn't on the curve, so I have to find (x,y) point on the curve that joins it and P as a tangent.

Any help? Thanks

2. Jan 16, 2008

### HallsofIvy

Staff Emeritus
First, write the point as (x0, y0) to distinguish from a general (x, y) point. Yes, the slope of a tangent line to the ellipse at that point is -x0/4y0 and so the equation of the tangent line is y= (-x0/4y0)(x- x0)+ y0. In order that that line go through (4, 0), you must have 0= (-x0/4y0)(4- x0)+ y0.

In order that P be on the ellipse it must also be true that x02/2+ y02= 1. That gives you two equations to solve for x0 and y0.

3. Jan 16, 2008

### Firepanda

I understood your 1st paragraph, but not so much the last sentence.

When you say in order that P be on the ellipse, I dont want it to be on the ellipse, I want it to be a point the tangent is connected to.

http://img142.imageshack.us/img142/6224/ellipsecm5.jpg [Broken]

Last edited by a moderator: May 3, 2017
4. Jan 16, 2008

### Firepanda

Nevermind I got it :D Thanks!