Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
99 Percentile Qs Bank for JEE MainMathematicsParabola

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

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 tangent to the same parabola at another point (x₁, y₁) on the parabola. If L and T are perpendic 2026Let O be the vertex of the parabola y^2=4x and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segment PQ is a conic C, then the len 2026Let chord PQ of length 3 13 of the parabola y^2 = 12x be such that the ordinates of points P and Q are in the ratio 1:2 . If the chord PQ subtends an angle at the focus of the para 2026Let the point P be the vertex of the parabola y = x^2 - 6x + 12 . If a line passing through the point P intersects the circle x^2 + y^2 - 2x - 4y + 3 = 0 at the points R and S , th 2026Let the directrix of the parabola P: y^2 = 8x , cut x -axis at the point A . Let B( , ) , > 1 , be a point on P such that the slope of AB is 3/5 . If BC is a focal chord of P , the 2026Let A,B and C be the vertices of a variable right angled triangle inscribed in the parabola y^2=16x . Let the vertex B containing the right angle be (4,8) and the locus of the cent 2026Consider the parabola P : y^2 = 4kx and the ellipse E : x^2 a^2 + y^2 b^2 = 1 . Let the line segment joining the points of intersection of P and E , be their latus rectums. If the 2026Let the parabola y = x^2 + px + q passing through the point (1, -1) be such that the distance between its vertex and the x -axis is minimum. Then the value of p^2 + q^2 is: 2026 Full Parabola list All 99 Percentile Qs Bank for JEE Main PYQs