The equation of a circle is x2 y2 R2 where R is the radius

The equation of a circle is x^2 + y^2 = R^2, where R is the radius of the circle. Write a program in a script file that first derives the equation (symbolically) of the tangent line to the circle at the point (x_0, y_0) on the upper part of the circle (i.e., for -R

Solution

% start the script

Syms x y R x0 y0;

M=-x0/y0;

S2=(y-y0)-m*(x-x0)

S2=subs (s2, y0, (R^2-x0^2)^0.5)

Y=solve (s2, y)

Mat lab output:

S2=y-y0+(x0*(x-x0))/y0

S2=

Y=- (R^2-x0^2)^(1/2)+(x0*(x-x0))/(R^2-x0^)^(1/2)

Y=-(x*x0-R^2)/(R^2-x0^2)^2(1/2)