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An ellipse centred at the origin has eccentricity 1/2 and one directrix x = -4. Find the equation of the normal to this ellipse at the point (1, 3/2).
- x + 2y = 4
- 2y - x = 2
- 4x - 2y = 1
- 4x + 2y = 7
Correct answer: 4x - 2y = 1
Solution
From e = 1/2 and directrix x = -4 the ellipse is x²/4 + y²/3 = 1; the normal at (1, 3/2) is 4x - 2y = 1.
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