Originally Posted by

**ukorov** (a)

(y - 5)/(x - 0) = (1 - 5)/(4 - 0) and then solve...

(b)

since AB (tangent to the circle) is perpendicular to CO (O is centre of circle and C is the point of contact between circle and AB), the product of the two slopes = -1

first find the slope of AB from the answer in (a), then use it to find the slope of CO.

then use the slope of CO and coordinates of O(5,4) to work out its equation.

(c) solve the two simultaneous equations obtained from (a) and (b)

(d) find the distance between O(5,4) and the answer from (c), which is the point of intersection between AB and CO. this distance is radius of circle. finally, use this radius r and O(5,4) to work out the equation of circle, ie:

(y - 4)^2 + (x - 5)^2 = r^2

and present answer in the form of Ax^2 + By^2 + Cx + Dy + constant = 0