Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202227 Jun 2022Evening ShiftMathematicsParabolaActual

If the equation of the parabola, whose vertex is at 5 , 4 and the directrix is 3 x + y - 29 = 0 , is x 2 + a y 2 + b x y + c x + d y + k = 0 , then a + b + c + d + k is equal to

Options

  1. A575
  2. B- 575
  3. C576
  4. D- 576

Correct answer

D. - 576

Step-by-step solution

Given the equation of the parabola whose vertex is 5 , 4 and equation of directrix is 3 x + y - 29 = 0 is x 2 + a y 2 + b x y + c x + d y + e = 0 Let focus be α , β Let equation of Z V which is perpendicular to 3 x + y - 29 = 0 be x - 3 y + k = 0 and it passes through point 5 , 4 . So, k = 7 and equation of Z V become x - 3 y + 7 = 0 Now the intersection of 3 x + y - 29 = 0   &   x - 3 y + 7 = 0 will be Z = 8 , 5 Now plotting the diagram we get, So, foot of perpendicular from 5 , 4 on 3 x +

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 Main PYQs