MATHS

(1) 8x – 2(k-1)y – 7 = 0 => slope = 8/[2(k-1)] = 4/(k-1)
2kx – 6y + 5 = 0 => slope = 2k/6 = k/3
The lines are parallel => 4/(k-1) = k/3
12 = k^2 – k
k^2 – k – 12 = 0
(k – 4)(k + 3) = 0
k = 4 or k = -3
(2) Mid-point of (2,-1) and (4,-2) is [(2+4)/2, (-1-2)/2] = (3, -1.5)
Slope of the line joining the 2 points = (-2+1)/(4-2) = -1/2
Slope of the perpendicular bisector = 2
Hence equation of perpendicular bisector is (y + 1.5)/(x – 3) = 2
y + 1.5 = 2x – 6
2y + 3 = 4x – 12
4x – 2y – 15 = 0
(3) f(x) is divisible by 3x-7 so 3x – 7 is a factor of f(x)
Therefore 3(x+2) – 7 is a factor of f(x+2)
Since 3(x + 2) – 7 = 3x + 6 – 7 = 3x – 1
Therefore 3x – 1 is a factor of f(x+2)