Question

Let a line L₁ be tangent to the hyperbola x²/16 - y²/4 = 1 and let L₂ be the line passing through the origin and perpendicular to L₁. If the locus of the point of intersection of L₁ and L₂ is (x² + y²)² = αx² + ßy², then α + ß is equal to_____.

Answer 1

Answer is 12

α = 16, ß = -4

α + ß = 16 - 4 = 12​