Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202524 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
24 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Parabola

JEE Main 2025 · 24 January · Evening Shift · Mathematics · Parabola

If the equation of the parabola with vertex V((3)/(2), 3) and the...

If the equation of the parabola with vertex V(32,3)andthedirectrix\mathrm{V}\left(\frac{3}{2}, 3\right) and the directrixx+2 y=0isis\alpha x^2+\beta y^2-\gamma x y-30 x-60 y+225=0,then, then\alpha+\beta+\gamma is equal to :

Options

  1. A7
  2. B9
  3. C8
  4. D6

Correct answer

B. 9

Step-by-step solution

∴ Equation of  parabola is PS=(1)PM⇒PS2=PM2(x−3)2+(y−6)2=(x+2y5)25x2−30x+5y2−60y+225=x2+4y2+4xy4x2+y2−4xy−30x−60y+225=0\begin{aligned} & \therefore \quad \text{ Equation\text{ 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 : α=4,β=1,γ=4∴α+β+γ=9\alpha=4, \beta=1, \gamma=4 \therefore \alpha+\beta+\gamma=9
Practice Parabola on Quantrex Academy →

More from Parabola

Let T be the tangent to the parabola y^2 = 16x at the point (64, 32) . Let L be the… JEE Advanced 2026Let O be the vertex of the parabola y^2=4x and its chords OP and OQ are perpendicular to… JEE Main 2026Let chord PQ of length 3 13 of the parabola y^2 = 12x be such that the ordinates of… JEE Main 2026Let the point P be the vertex of the parabola y = x^2 - 6x + 12 . If a line passing… JEE Main 2026Let the directrix of the parabola P: y^2 = 8x , cut x -axis at the point A . Let B(α, β)… JEE Main 2026Let A,B and C be the vertices of a variable right angled triangle inscribed in the… JEE Main 2026Consider the parabola P : y^2 = 4kx and the ellipse E : (x^2)/(a^2) + (y^2)/(b^2) = 1 .… JEE Main 2026Let the parabola y = x^2 + px + q passing through the point (1, -1) be such that the… JEE Main 2026Let A be the focus of the parabola y^ 2 =8 x . Let the line y=m x+c intersect the… JEE Main 2026Let the image of parabola x^ 2 =4 y , in the line x-y=1 be (y+a)^ 2 =b(x-c) , a, b, c ∈… JEE Main 2026An equilateral triangle OAB is inscribed in the parabola y^ 2 =4 x with the vertex O at… JEE Main 2026Let the locus of the mid-point of the chord through the origin O of the parabola y^ 2 =4… JEE Main 2026If the chord joining the points P_ 1 (x_ 1 , y_ 1 ) and P_ 2 (x_ 2 , y_ 2 ) on the… JEE Main 2026Let y^ 2 =12 x be the parabola with its vertex at O. Let P be a point on the parabola and… JEE Main 2026Let one end of a focal chord of the parabola y^ 2 =16 x be (16,16) . If P(α, β) divides… JEE Main 2026Let O be the vertex of the parabola x^ 2 =4 y and Q be any point on it. Let the locus of… JEE Main 2026 Full Parabola list Parabola JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs