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Find the locus of the foot of the perpendicular drawn from the centre of the ellipse x² + 3y² = 6 to any tangent of the ellipse.

1. (x² + y²)² = 6x² + 2y²
2. (x² - y²)² = 6x² - 2y²
3. (x² + y²)² = 6x² - 2y²
4. (x² - y²)² = 6x² + 2y²

Correct answer: (x² + y²)² = 6x² + 2y²

Solution

The pedal curve of an ellipse with respect to its centre is (x² + y²)² = a²*x² + b²*y²; substituting a² = 6, b² = 2 gives the answer.

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