C1- AS Maths Circle Question Help

i) Looking at the circle equation, you can work out the coordinates. I.e X-3=0, therefore x co-ordinate is..... Y+2=0, therefore y co-ordinate is....

ii) Put (6,-6) into the equation of the circle.

iii) Using part (i) and (6,-6), work out the gradient of the tangent and then the equation using y-y1=m(x-x1)

iv) Draw a diagram, it really is that easy. Basically, it is (6, -6), 10 across, so the x-coordinate will vary. You know it (the equation) =100 as radius is 10. Have fun.

11 A circle has equation (x − 3)^2 + (y + 2)^2 = 25.

(i) State the coordinates of the centre of this circle and its radius. [2]

(ii) Verify that the point A with coordinates (6, −6) lies on this circle. Show also that the point B on the circle for which AB is a diameter has coordinates (0, 2). [3]

(iii) Find the equation of the tangent to the circle at A. [4]

(iv) A second circle touches the original circle at A. Its radius is 10 and its centre is at C, where BAC is a straight line. Find the coordinates of C and hence write down the equation of this second circle. [3]

I've done all parts apart from iv). I'd be very grateful if someone could explain how to do part iv) in detail.

Thanks very much.