Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202225 Jun 2022Morning ShiftMathematicsParabolaActual

If y = m 1 x + c 1 and y = m 2 x + c 2 , m 1 ≠ m 2 are two common tangents of circle x 2 + y 2 = 2 and parabola y 2 = x , then the value of 8 m 1 m 2 is equal to

Options

  1. A3 2 - 4
  2. B6 2 - 4
  3. C- 5 + 6 2
  4. D3 + 4 2

Correct answer

A. 3 2 - 4

Step-by-step solution

Equation of the tangent to the parabola can be written as y = m x + 1 4 m or y - m x - 1 4 m = 0 Now, the perpendicular distance from 0 , 0 to the tangent is equal to the radius of the given circle, so O M = 2 ⇒ - 1 4 m 1 + m 2 = 2 ⇒ 2 16 m 2 1 + m 2 = 1    ⇒ 32 m 4 + 32 m 2 - 1 = 0 ⇒    m 2 = - 2 5 + 2 3 16 + 2 2 × 2 5 ignoring the negative sign as it is square function. Now 8 m 1 m 2 = 8 m 2 = - 2 5 + 2 3 16 + 2 2 3 = 3 2 - 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