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 y-axis. 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.
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.
b) The y-axis equation is x=0
The circle cuts the y-axis for the coordinates satisfying both
x=0 and x² + y² - 4x - 2y - 20 = 0
thus x=0 and y²-2y-20=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 and passes through A