State the correct answer... P(x1,y1) is a point on the circle x^2+y^2 = r^2

State the correct answer...
P(x1,y1) is a point on the circle x^2+y^2 = r^2. The Tangent at P:

A) has equation x1x + y1y = r^2
B) doesn't have equation x1x + y1y = r^2

Please help with working out!

Ans::
x^2+y^2 = r^2 take derivative w.r.t x
2x+2y dy/dx=0
or, dy/dx=-x/y


Therefore, dy/dx at point(x1,y1)
dy/dx=-x1/y1

now the equation of the tangent,
y-y1=-x1/y1(x-x1)
or, yy1-y1^2=-xx1+x1^2
or, xx1+yy12=x1^2+y1^2=r^2 [(x1,y1) is a point on the circle]

So, the answer is A) has equation x1x + y1y = r^2.