Intersection of a known line and two lines with an unknown variable in each.

I'm trying to do number 7 on page 10 of this document: http://www.edexcel.com/migrationdocu...athematics.pdf

I have done parts a and b. The answers give x=-4 but I don't know how that is obtained.

The method used for part b is questionable as I would use implicit differentiation. You cannot simply convert to an expression starting with y= when that type of equation isn't suitable. It is also questionable why the value of a is not used in b but that is a minor point.

Re: Intersection of a known line and two lines with an unknown variable in each.

This is in the wrong sub-forum. You should post this in the university math board.

Re: Intersection of a known line and two lines with an unknown variable in each.

It is pre-university mathematics since it is a question from A-level.

Re: Intersection of a known line and two lines with an unknown variable in each.

I thought you meant that you needed help with implicit differentiation.

Re: Intersection of a known line and two lines with an unknown variable in each.

Re: Intersection of a known line and two lines with an unknown variable in each.

I am trying to do part c. I have figured there is an infinite number of points on the line y=15 where x<0 that could be the point of intersection. The answers give x=-4 which is presumably the nearest point that allows t in both of the tangents to be an integer or a rational number. The question does not give enough information to solve the coordinates of A and B.

Re: Intersection of a known line and two lines with an unknown variable in each.

Hi Stuck Man! :)

I'm afraid your assumption about x=-4 is incorrect.

There is a piece of information in the problem that you have not used yet.

It says that both tangent lines meet on *the directrix* of C where y=15.

The parabola has a directrix at x=-a.

In other words, both tangents go through the point (-4,15).

For the meaning of the word *directrix*, see for instance: Conic section - Wikipedia, the free encyclopedia.