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AP EAMCET202318 May 2023Morning ShiftMathematicsParabolaActual

If (2,3) is the vertex and.' (3,2) is the focus of a parabola, then its equation is

Options

  1. Ax^2+2 x y+y^2-18 x-2 y+35=0
  2. B2 x^2+4 x y+2 y^2-9 x-y+17=0
  3. Cx^2+2 x y+y^2-18 x-2 y+17=0
  4. Dx^2+4 x y+4 y^2-18 x+2 y+9=0

Correct answer

C. x^2+2 x y+y^2-18 x-2 y+17=0

Step-by-step solution

Vertex O (2,3) focus S (3,2) O is the mid point AS x ₁+3 2 =2 and y ₁+2 2 =3 x₁=1, y₁=4 Slope of AS, m₁= 2-3 3-2 =-1 Directrix is perpendicular to axis of parabola: m ₂=1 m ₂ . is slope of directrix (y-y₁ )=m₂ (x-x₁ ) y-4=1(x-1) y-x=3 ...(i) Let point P is on parabola Since, M P=P S . as M is foot of ^ r from P to the directrix. aligned & y-x-3 1+1 = (x-3)^2+(y-2)^2 & (y-x-3)^2=2 ((x-3)^2+(y-2) )^2 & x^2+y^2-18 x-2 y+2 x y+17=0 aligned

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