JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the equation of the parabola with vertex \(\mathrm{V}\left(\frac{3}{2}, 3\right)\) and the directrix \(x+2 y=0\) is \(\alpha x^2+\beta y^2-\gamma x y-30 x-60 y+225=0\), then \(\alpha+\beta+\gamma\) is equal to :
- A 7
- B 9
- C 8
- D 6
Answer & Solution
Correct Answer
(B) 9
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \therefore \quad \text { Equation of parabola is } P S=(1) P M \\ & \Rightarrow P S^2=P M^2 \\ & (x-3)^2+(y-6)^2=\left(\frac{x+2 y}{\sqrt{5}}\right)^2 \\ & 5 x^2-30 x+5 y^2-60 y+225=x^2+4 y^2+4 x y \\ & 4 x^2+y^2-4 x y-30 x-60 y+225=0 \end{aligned}\) We get :…
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