If the equation of the parabola with vertex V ( 2 3 , 3 ) and the directrix x + 2 y = 0 is α x 2 + β y 2 − γ x y − 30 x − 60 y + 225 = 0 , then α + β + γ is equal to :

Question

If the equation of the parabola with vertex V ( 2 3 ​ , 3 ) and the directrix x + 2 y = 0 is α x 2 + β y 2 − γ x y − 30 x − 60 y + 225 = 0 , then α + β + γ is equal to :

TestHub · Accepted Answer

​ ∴ Equation of parabola is PS = ( 1 ) PM ⇒ P S 2 = P M 2 ( x − 3 ) 2 + ( y − 6 ) 2 = ( 5 ​ x + 2 y ​ ) 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 ​ We get : α = 4 , β = 1 , γ = 4 ∴ α + β + γ = 9

Mathematics - Parabola Question with Solution | TestHub

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