So, I have the ellipse: $3x^2+4y^2=5$ and want to decide the equation of a line that tangent the ellipse at the point $(1, \frac {\sqrt 2} 2)$. So I use implicit differentiation of the ellipse and get that $ \frac {dy} {dx} $ is $ -\frac {3x} {4y} $.
After that I put the x and y values from the point in (this is where I suppose I'm doing something wrong) to get the slope at that point. With this I get:
$ - \frac {3(1)} {4( \frac {\sqrt 2} {2}) } $ which gives me: $ - \frac {3} {2 \sqrt 2} $ which is wrong so it screws up the rest of my calculations.
How am I suppose to do this instead? As written above, I suspect that my mistake is when I put the x and y values from the point in.