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
Explanation
(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