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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.
- (x² + y²)² = 6x² + 2y²
- (x² - y²)² = 6x² - 2y²
- (x² + y²)² = 6x² - 2y²
- (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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