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Question:

The equation of a tangent to the hyperbola 4x² - 5y² = 20 parallel to the line x - y = 2 is?

x - y + 7 = 0

x - y + 1 = 0

x - y + 9 = 0

x - y - 7 = 0

Solution:

Hyperbola:
4x² - 5y² = 20
Dividing by 20, we get
x²/5 - y²/4 = 1
Slope of tangent = 1
Equation of tangent: y = x ± √(5 + 4)
=> y = x ± 3
=> y = x + 3 or y = x - 3
=> x - y + 3 = 0 or x - y - 3 = 0