Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main20253 Apr 2025Morning ShiftMathematicsParabolaActual

The radius of the smallest circle which touches the parabolas y=x^2+2 and x=y^2+2 is

Options

  1. A7 2 2
  2. B7 2 16
  3. C7 2 4
  4. D7 2 8

Correct answer

D. 7 2 8

Step-by-step solution

The given parabolas are symmetric about the line y=x Tangents at A & ~B must be parallel to y = x line, so slope of the tangents =1 ( d y d x )_ A =1= ( d y d x )_ B For point B , y = x ^2+2 gathered d y d x =2 x=1 x= 1 2 y= 9 4 Point B= ( 1 2 , 9 4 ) Point A = ( 9 4 , 1 2 ) AB = ( 1 2 - 9 4 )^2+ ( 9 4 - 1 2 )^2 = 98 16 = 7 2 4 gathered Radius == 7 2 8

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