If the equation of the hyperbola with foci $(4, 2)$ and $(8, 2)$ is $3x^2 - y^2 - \alpha x + \beta y + \gamma = 0$, then $\alpha + \beta + \gamma$ is equal to __________.

JEE Main 2025 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 3 April 2025, Shift 2, Maths Q23

Question 23 of 75 in this shift, Maths question 23 of 25, Section B.

If the equation of the hyperbola with foci

(4, 2)

and

(8, 2)

3x^2 - y^2 - \alpha x + \beta y + \gamma = 0

, then

\alpha + \beta + \gamma

is equal to __________.

Official answer

141

NTA final key.