If the equation of the hyperbola with foci $(4, 2)$ and $(8, 2)$ is $3 x^{2} - y^{2} - αx + β y + γ = 0$ , then $α + β + γ$ is equal to _____.

Question

If the equation of the hyperbola with foci ( 4 , 2 ) and ( 8 , 2 ) is 3 x 2 − y 2 − αx + β y + γ = 0 , then α + β + γ is equal to _____.

TestHub · Accepted Answer

Equation of hyperbola is a 2 ( x − 6 ) 2 ​ − 4 − a 2 ( y − 2 ) 2 ​ = 1 ⇒ ( 4 − a 2 ) ( x − 6 ) 2 − a 2 ( y − 2 ) 2 = a 2 ( 4 − a 2 ) comparing with 3 x 2 − y 2 − αx + β y + γ = 0 , we get a 2 = 1 and α = 36 , β = 4 and γ = 101 ∴ α + β + γ = 141

Mathematics - Hyperbola Question with Solution | TestHub

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