Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main20252 Apr 2025Evening ShiftMathematicsParabolaActual

Let the point P of the focal chord P Q of the parabola y^2=16 x be (1,-4) . If the focus of the parabola divides the chord PQ in the ratio m : n , gcd (m, n)=1 , then m^2+n^2 is equal to :

Options

  1. A17
  2. B10
  3. C37
  4. D26

Correct answer

A. 17

Step-by-step solution

y^2=16 x ; a=4 focus S (4,0) aligned & 2 at ₁=-4 & 2(4) t ₁=-4 & t ₁=- 1 2 & t ₁ t ₂=-1 aligned aligned & t ₂=2 & Q ( at ₂^2, 2 at ₂ )=(16,16) aligned Let, S divides PQ internally in : 1 ratio aligned & 16 -4 +1 =0 & = 1 4 = m n & ~m ^2+ n ^2=1+16=17 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 JEE Main PYQs