Finding the tangent line of an ellipse

I have to find the tangent line of an ellipse that I have written code for. The ellipse is parametrized, so I'm not sure how to write the code to find the tangent line. This is waht I have so far. What do you recommend I add to find the tangent line at the point (x(a),y(a))? Please respond as soon as possible.

function destin_ellipse(xRadius,yRadius)
c=sqrt(xRadius^2-yRadius^2);
theta = [0 : 0.01 : 2*pi]';
x = xRadius * cos(theta);
y = yRadius * sin(theta);
a=randi(300);
clf;
plot(x, y, 'LineWidth', 1);
hold on;
plot(x(a),y(a),'r.');
plot([-c x(a)],[0 y(a)],'g');
plot([c x(a)],[0 y(a)],'g');
plot(c,0,'r.');
plot(-c,0,'r.');
axis square;
grid on;
if xRadius>yRadius
    xlim([-(xRadius+1), xRadius+1]); ylim([-(xRadius+1), xRadius+1])
else
    xlim([-(xRadius+1), xRadius+1]);
    ylim([-(yRadius+1), yRadius+1]);
end

Answer 1

[KSSV]

https://in.mathworks.com/matlabcentral/answers/89306-tangent-line-to-a-curve-at-a-given-point

[Destin Davis]

Thank you. This was helpful, however my problem involves a parametrized version of the ellipse's equation, so I don't think this would work too well for me. Thank you, though.

[darova]

Since tangens of an angle:

[Destin Davis]

Thank you so much. But with this derivative, how would I plot the tangent line at my point (x(a),y(a))?

[darova]

What do you know about equation of a straight line?