SOLUTION: show that the line y=2x+3 is the equation of the tangent of the ellipse 4x^2+2y^2=2. hence find the coordinate of the point of contact

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: show that the line y=2x+3 is the equation of the tangent of the ellipse 4x^2+2y^2=2. hence find the coordinate of the point of contact      Log On


   

Question 798328: show that the line y=2x+3 is the equation of the tangent of the ellipse 4x^2+2y^2=2. hence find the coordinate of the point of contact
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
You would expect exactly one intersection point. Substitute for y and solve for x.

4x%5E2%2B2%282x%2B3%29%5E2=2, that substitution done,
2x%5E2%2B%282x%2B3%29%5E2=1
2x%5E2%2B4x%5E2%2B12x%2B9=1
6x%5E2%2B12x%2B8=0
3x%5E2%2B6x%2B4=0

x=%28-6%2B-sqrt%2836-4%2A3%2A4%29%29%2F%282%2A3%29
x=%28-6%2B-sqrt%2836-48%29%29%2F%282%2A3%29
x=%28-6%2B-sqrt%28-12%29%29%2F%282%2A3%29
x=%28-3%2B-+i%2Asqrt%283%29%29%2F%283%29, apparently NOT tangent! A COMPLEX solution!

I've checked this over twice. You would not be expecting a complex solution, but you want instead a single real solution. One of your equations must be wrong.


A better look at the graph: