2019 WAEC Further Mathematics Theory The curve y = 7 - \(\frac{6}{x}\) and the line y + 2x - 3...

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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