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Jee Main 2025 — Medium JEE math MCQ

If the equation of the parabola with vertex \(V\left(\frac{3}{2}, 3\right)\) and the directrix \(x + 2y = 0\) is \(\alpha x^2 + \beta y^2 - \gamma xy - 30x - 60y + 225 = 0\), then \(\alpha + \beta + \gamma\) is equal to
  1. A. 7
  2. B. 9
  3. C. 8
  4. D. 6 \(\alpha x^2 + \beta y^2 - \gamma xy - 30x - 60y + 225 = 0\)

Solution

The correct option is **B**. (B. 9)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
If the equation of the parabola with vertex V(32,3)V\left(\frac{3}{2}, 3\right) and the directrix x+2y=0x + 2y = 0 is αx2+βy2−γxy−30x−60y+225=0\alpha x^2 + \beta y^2 - \gamma xy - 30x - 60y + 225 = 0, then α+β+γ\alpha + \beta + \gamma is equal to
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep