
Circle Geometry
Circle Diagram  http://i39.tinypic.com/33z48yq.png
1. The diagram shows a circle with centre (2,1) and radius 5.
a) Show that the equation of the circle may be written as:
x^2 + y^2  4x  2y  20 = 0
b) Find the coordinates of the Points P and Q where the circle cuts the yaxis. Leave your answers in the form a(+ or ) sqrt [b].
c) Verify the point A (5,3) lies on the circle.
Show that the tangent to the circle at A has equation 4y = 3x  27.
Thanks!

Okay, I have worked out part a) by completing the square. (x  2)^2 + (y  1)^2 = 25
I still can't understand part b) or c) though.

Hi
b) The yaxis equation is x=0
The circle cuts the yaxis for the coordinates satisfying both
x=0 and x² + y²  4x  2y  20 = 0
thus x=0 and y²2y20=0
c) You just need to show that both x=5 and y=3 satisfy the equation x² + y²  4x  2y  20 = 0
The tangent to the circle at A is perpendicular to $\displaystyle \overrightarrow{CA}$ and passes through A