Question

The line 2x + 3y = 8 meets the curve 2x² + 3y² = 110 at the points of A and B. Find the coordinates of A and B.

Answer 1

From (1), we get x = (8 - 3y) / 2 ––(3)

Substitute (3) into (2),

2 [(8 - 3y) / 2]² + 3y² = 110

(8 - 3y)² + 3y² = 220

15y² - 48y - 156 = 0

Therefore y = 5.2, then x = (8 - 3×5.2) / 2 = -3.8

OR y = -2, then x = [8 - 3×(-2)] / 2 = 7

The cordinates of A and B are (-3.8, 5.2) and (7, -2).

Answer 2

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