If the line 2 x + 6 y = 2 touches the hyperbola x 2 - 2 y 2 = a 2 , then a 2 is equal to

Question

If the line 2 x + 6 y = 2 touches the hyperbola x 2 - 2 y 2 = a 2 , then a 2 is equal to,

MARKS App · Accepted Answer

The tangent to the hyperbola is y = - 2 6 x + 2 6 Also, tangent to hyperbola in slope form is y = m x ± a 2 m 2 - b 2 i.e. 2 6 = a 2 - 2 6 2 - a 2 2 On squaring, we get, 4 6 = a 2 ⋅ 4 6 − a 2 2 ⇒ 2 3 = a 2 6 ⇒ a 2 = 4

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