Theory question 109
Coordinate GeometryThe curve y = 7 − 6/x and the line y + 2x − 3 = 0 intersect at two points. Find the: (a) coordinates of the two points; (b) equation of the perpendicular bisector of the line joining the two points.
Show the model answer
Model answer
(a) 7 − 6/x = 3 − 2x gives 2x² + 4x − 6 = 0, i.e. x² + 2x − 3 = 0, x = 1 or −3. Points (1, 1) and (−3, 9).
(b) Midpoint (−1, 5); the joining line has gradient −2, so the bisector has gradient ½.
y − 5 = ½(x + 1), i.e. 2y − x − 11 = 0.
Explanation
The perpendicular bisector passes through the midpoint with gradient −1/m.