TylerRayAdams8054 TylerRayAdams8054
  • 25-01-2024
  • Mathematics
contestada

If the tangent drawn to the hyperbola 4y² = x² + 1 intersect the co-ordinate axes at the distinct points A and B, then the locus of the mid-point of AB is:

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andyzhuangzixian andyzhuangzixian
  • 25-01-2024

Answer:  (0, 0)

Step-by-step explanation:

Given the equation of the hyperbola: 4y² = x² + 1

4(0)² = x² + 1

0 = x² + 1

x² = -1

4y² = 0² + 1

4y² = 1

y² = 1/4

y = ±1/2

Midpoint = ( (x₁ + x₂)/2 , (y₁ + y₂)/2 )

Midpoint = ( (0 + 0)/2 , (1/2 + (-1/2))/2 )

Midpoint = (0, 0)

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