Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202330 Jan 2023Evening ShiftMathematicsParabolaActual

Let A be a point on the x -axis. Common tangents are drawn from A to the curves x 2 + y 2 = 8 and y 2 = 16 x . If one of these tangents touches the two curves at Q and R , then Q R 2 is equal to

Options

  1. A64
  2. B76
  3. C81
  4. D72

Correct answer

D. 72

Step-by-step solution

Let a tangent on parabola y 2 = 16 x be, y = m x + 4   m It is also common to x 2 + y 2 = 8 If   4 m 2 = 8 1 + m 2 ⇒ 16 m 2 = 8 ( 1 + m 2 ) ⇒ m 4 + m 2 - 2 = 0 ⇒ ( m 2 + 2 ) ( m 2 - 1 ) = 0 ⇒ m = ± 1 Taking one of the tangents y = x + 4 ⇒ x - y + 4 = 0 Tangent to x 2 + y 2 = 8 is x x 1 + y y 1 - 8 = 0 ∴ x 1 1 = y 1 1 = - 8 4 ⇒ Q ( - 2 , 2 ) Tangent to y 2 = 16 x is y y 1 = 8 ( x + x 1 ) ⇒ 8 x - y y 1 + 8 x 1 = 0 ∴ 8 1 = - y 1 - 1 = 8 x 1 4 ⇒

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