Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Parabola

NTA Abhyas 2020 · Mathematics · Parabola

The equation of parabola which cuts the parabola y^ 2 = 4bx...

The equation of parabola which cuts the parabola y2=4bxy^{2} = 4bx orthogonally having the same axis and length of latus rectum as 8b8b, is

Options

  1. Ay2=−8b(x−8b)y^{2} = - 8b \left(x - 8b\right)
  2. By2=−8b(x−4b)y^{2} = - 8b \left(x - 4b\right)
  3. Cy2=−8b(x−32b)y^{2} = - 8b \left(x - 32b\right)
  4. Dy2=−8b(x−3b)y^{2} = - 8b \left(x - 3b\right)

Correct answer

D. y2=−8b(x−3b)y^{2} = - 8b \left(x - 3b\right)

Step-by-step solution

Focus of parabola y2=4bxy^{2} = 4bx is \left(b, 0\right)<br/>Focusofparabolainoption(A)<br />Focus of parabola in option \left(A\right) is \left(6b, 0\right)<br/>Focusofparabolainoption(B)<br />Focus of parabola in option \left(B\right) is \left(2b, 0\right)<br/>Focusofparabolainoption(C)<br />Focus of parabola in option \left(C\right) is \left(30b, 0\right)<br/>Focusofparabolainoption(D)<br />Focus of parabola in option \left(D\right) is \left(b, 0\right)<br/>Hence,option(D)<br />Hence, option \left(D\right) is correct
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… JEE Advanced 2026Let O be the vertex of the parabola y^2=4x and its chords OP and OQ are perpendicular to… JEE Main 2026Let chord PQ of length 3 13 of the parabola y^2 = 12x be such that the ordinates of… JEE Main 2026Let the point P be the vertex of the parabola y = x^2 - 6x + 12 . If a line passing… JEE Main 2026Let the directrix of the parabola P: y^2 = 8x , cut x -axis at the point A . Let B(α, β)… JEE Main 2026Let A,B and C be the vertices of a variable right angled triangle inscribed in the… JEE Main 2026Consider the parabola P : y^2 = 4kx and the ellipse E : (x^2)/(a^2) + (y^2)/(b^2) = 1 .… JEE Main 2026Let the parabola y = x^2 + px + q passing through the point (1, -1) be such that the… JEE Main 2026Let A be the focus of the parabola y^ 2 =8 x . Let the line y=m x+c intersect the… JEE Main 2026Let the image of parabola x^ 2 =4 y , in the line x-y=1 be (y+a)^ 2 =b(x-c) , a, b, c ∈… JEE Main 2026An equilateral triangle OAB is inscribed in the parabola y^ 2 =4 x with the vertex O at… JEE Main 2026Let the locus of the mid-point of the chord through the origin O of the parabola y^ 2 =4… JEE Main 2026If the chord joining the points P_ 1 (x_ 1 , y_ 1 ) and P_ 2 (x_ 2 , y_ 2 ) on the… JEE Main 2026Let y^ 2 =12 x be the parabola with its vertex at O. Let P be a point on the parabola and… JEE Main 2026Let one end of a focal chord of the parabola y^ 2 =16 x be (16,16) . If P(α, β) divides… JEE Main 2026Let O be the vertex of the parabola x^ 2 =4 y and Q be any point on it. Let the locus of… JEE Main 2026 Full Parabola list Parabola JEE Maths PYQsJEE Mathematics PYQs All NTA Abhyas JEE Main PYQs