I´m sorry, I´m stuck here.
##M(x,y) = ( \begin{array} {c} a*cos(t) \\ b*sin(t) \end{array} )##
##M_0## is what I´m trying to work out.
So the determinant of ##M_0M## and ##f'(t_0)## is ##det ( \begin{array} {cc} a*cos(t)-M_0 & -(a*y_0)/b \\ b*sin(t)-M_0 & (b*x_0)/a \end{array} ) =...
if ##M_0=f(t_0)## , then ##{M_0M}## and ##f'(t_0)## are collinear, so the determinant must be zero. That means that
det ( ## \begin{array}{ccc}
t-x_0 & -(a*y_0)/b \\
t-y_0 & (b*x_0)/a
\end{array} ## ) = (t-x_0)*(b*x_0)/a + (a*y_0)/b * t-y_0 =0Am I on the right track?
Thank you. So the tangent and normal vectors are correct?
How do I work out the vector line directed by the tangent vector at ##M_0## ? The tangent vector is (-ay/b , bx/a), how do I work out a line from that?
Homework Statement
The ellipse is given as (x^2/a^2) + (y^2/b^2)=1
I´m meant to calculate a tangential vector, a normal vector and find an equation for the tangent using a random point (x0,y0).
I´m meant to do this in 2 ways: firstly by using the parametrization x(t)=a*cos(t) and...