The curve y = 7 - \(\frac{6}{x}\) and the line y + 2x - 3 = 0 intersect at two point. Finf the;
(a) coordinates of the two points
(b) equation of the perpendicular bisector of the line joining the two points
(a) 7 - \(\frac{6}{x} = 3 - 2x\)
Simplifying; \(x^2 + 2x - 2 = 0\)
x = 1 or x = -3
Substituting for x; y = 3 - 2(1) = 3 - 2 = 1 or y = 3 - 2(-3) = 3 + 6 = 9
The coordinate of the two points are (x y) = (1, 1), (-3, 9)
(b) (\(\frac{1 - 3}{2}, \frac{1 + 9}{2}\)) = (-1, 5)
The gradient of the point of intersection ; \(\frac{9 - 1}{-3 -1} = \frac{8}{-4}\) = -2
The gradient of the perpendicular bisector; \(\frac{1}{2}\)
Thus, the equation of the perpendicular bisector; y - 5 = \(\frac{1}{2}\) (x + 1)
Therefore, 2y - x - 11 = 0
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