Question

Please help me check my work. I needed the equation for the tangent line to the elipse 2x^2 + y^2 = 3 and that was parallel to 2x + y = 5.

Answer 1

I first wrote it like this:

r: (x,y) = (x0,y0) + lambda v, where v gradient f(x0,y0) = 0.

gradient of f(x,y) = (4x,2y)
gradient of f(x0,y0) = (4x0,2y0)

Answer 2

Then I did the same with 2x + y = 5

r2: (x,y) = (x1,y1) + t u

gradient of f(x,y) = (2,1)
gradient of f(x1,y1) = (2,1)

u = (-1,2)

v is parallel to (2,1), so for some value of h, v = h (-1,2)

v = (2y0,-4x0)

2y0 = - h
-4x0 = 2h

y0 = -h/2
x0 = -h/2

h = -2

y0 = 1
x0 = 1

Answer 3

r: (x,y) = (1,1) + lambda (2,-4)

Answer 4

I'm not sure if it's right though...