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## 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 y(t)=b*sin(t) and secondly by solving the equation for x or y.

## Homework Equations

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The formula for a tangential vector is ((dx/dt) , (dy/dt)).

The formula for a normal vector is +- ((dx/dt) , (dy/dt))/||((dx/dt) , (dy/dt))||

The tangent is linear, so it should have the form y=kx+d

## The Attempt at a Solution

x(t)=a*cos(t) and y(t)=b*sin(t), so the tangential vector is ((dx/dt) , (dy/dt)) = (-a*sin(t), b*cos(t)) = (-ay/b , bx/a)

||((dx/dt) , (dy/dt))|| = \sqrt{(ay/b)^2 + (bx/a)^2} , so the normal vector is (-ay/b , bx/a)/(\sqrt{(ay/b)^2 + (bx/a)^2})

I´m not sure how to find an equation for the tangent. I can use y=kx+d and I think that k is (-(a*y0)/b , (b*x0)/a) , but I don´t know how to continue from there.

For the second part:

x = \sqrt{a^2- (y^2*a^2)/b^2}

y= \sqrt{b^2-(x^2*b^2)/a^2}

So do I just have to calculate (dx/dy, dy/dx) now?