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Coordinate Geometry Questions

The points X and Y have coordinates (0,3) and (6,11) respectively. XY is a chord of a circle C with centre Z.

a) Find the gradient of XY.

The point M is the midpoint of XY

b) find an equation for the line which passes through Z and M.

Given that the y coordinate of Z is 10

c) find the x coordinate of Z

d) find the equation of the circle C, giving your answer in the form x^2+y^2+ax+by+c=0 where a, b and c are constants.
Where are you stuck?
a) Change in y divided by the change in x
(11-3)/(6-0) = 4/3

b) Find the midpoint M(3,7)
The line ZM is perpendicular to the line XY, meaning that the gradients of the two lines multiply to make -1, which makes the gradient of ZM -3/4.
y = -3/4x + c
'plug' the coordinates of M into this.
7 = -3/4(3) + c
c = 37/4
y = -3/4 x+ 37/4

c) 10 = -3/4x +37/4
3/4 = -3/4x
x = -1

d) Use Pythagoras' theorem to work out the lengths of ZM and YM
ZM:
4^2 + 3^2 = 25 (5^2)
ZM=5

YM:
3^2 + 4^2 =35 (5^2)
YM=5