中五數學題請教 已知答案但唔識點解?

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1.
x² + y² + 10x = 0
The centre is (-10/2,0) = (-5,0)

The slope of the chord = -1 / { (-1/2 - 0) / [-3/2 - (-5)] } = -1 / (-1/7) = 7
The equation of the chord：
y - (-1/2) = 7 [x - (-3/2)]
y + 1/2 = 7x + 21/2
7x - y + 10 = 0

2.
Suppose the equation of C is x² + y² + (5 - k)x - (k + 3)y + 3k = 0

The centre is (- (5 - k)/2 , - [- (k + 3)]/2 )
Since the centre of C lies on the x-axis, the y - coordinate is 0
- (k + 3)/2 = 0
k + 3 = 0
k = -3
The x - coordinate is - (5 - k)/2 = - [5 - (-3)]/2 = -4

x² + y² + [5 - (-3)]x - (-3 + 3)y + 3(-3) = 0
x² + y² + 8x - 9 = 0
(x² + 8x + 16) + y² = 9 + 16
(x + 4)² + y² = 25
(x + 4)² + y² = 5²

The radius of C = 5