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

A parabola having its axis parallel to Y -axis, passes through the points (0, 2 5 ),(4,-2) and (1, 8 5 ) ; Then a point that lies on this parabola is

Options

  1. A(3,5 / 2)
  2. B(-1,2)
  3. C(-2,28 / 5)
  4. D(2,8 / 5)

Correct answer

D. (2,8 / 5)

Step-by-step solution

Since, the axis of the parabola is parallel to y-axis. Then, (x-h)^2=4 a(y-k) Since, e q^ n (i) passes through the given points (0, 2 5 ) , (4,-2) & (1, 8 5 ) h ^2=4 a ( 2 5 - k ) (4-h)^2=4 a(-2-k) (1-h)^2=4 a ( 8 5 -k ) Solving eqn. (ii), (iii) & (iv), we get h = 3 2 , k = 7 4 , a =- 5 12 Putting above values in eqn. (i), we get (x- 3 2 )^2=- 5 3 (y- 7 4 ) Let's check the point (2, 8 5 ) on equation (v): 1 4 = 1 4 ; (2, 8 5 ) lies on the parabola.

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