Question

The value of m for which y = mx + 6 is a tangent to the hyperbola (x²/100) – (y²/49) = 1 is

(a) √(17/20)

(b) √(20/3)

(c) √(20/17)

(d) √(3/20)   

Answer 1

The correct option (a) √(17/20)

Explanation:

hyperbola is (x²/100) – (y²/ 9) = 1

Tangent is y = mx + 6.

For this to be tangent c² = a²m² – b²

i.e.       6² = (100)m² – 49

∴    (85/100) = m² ⇒ m = √(17/20).