Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced2006MathematicsParabolaActual

Axis of a parabola is y=x and vertex and focus are at a distance 2 and 2 2 respectively, from the origin. Then, equation of the parabola is

Options

  1. A(x-y)^2=8(x+y-2)
  2. B(x+y)^2=2(x+y-2)
  3. C(x-y)^2=4(x+y-2)
  4. D(x+y)^2=2(x-y+2)

Correct answer

A. (x-y)^2=8(x+y-2)

Step-by-step solution

As distance of vertex from origin is 2 and focus is 2 2 . V(1,1) and F(2,2) [i.e. lying on y=x ] where, length of latusrectum aligned & =4 a, & =4 2 aligned [ where a= 2 ] By definition of parabola P M^2=(4 a)(P N) where, P N is length of perpendicular upon x+y-2=0 [i.e. tangent at vertex] array ll & (x-y)^2 2 =4 2 ( x+y-2 2 ) & (x-y)^2=8(x+y-2) array Hence, the equation of parabola is (x-y)^2=8(x+y-2) .

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 JEE Advanced PYQs