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The locus of the feet of the perpendiculars drawn from the centre of the hyperbola x² - 4*y² = 4 onto its variable normals has the equation (x² + y²)² * (4*y² - x²) = lambda * x² * y². Find lambda.
- 25
- 16
- 9
- 4
Correct answer: 25
Solution
Eliminating the parameter from the foot of the perpendicular from the centre to the variable normal yields lambda = (a² + b²)² = (4 + 1)² = 25.
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