Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 201911 JanuaryMorning Shift
Exam
JEE Main
Year
2019
Date
11 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Hyperbola

JEE Main 2019 · 11 January · Morning Shift · Mathematics · Hyperbola

Equation of a common tangent to the parabola y^ 2 =4 x and the...

Equation of a common tangent to the parabola y2=4xy^{2}=4 x and the hyperbola xy=2x y=2 is :

Options

  1. Ax+y+1=0x+y+1=0
  2. Bx−2y+4=0x-2 y+4=0
  3. Cx+2y+4=0x+2 y+4=0
  4. D4x+2y+1=04 x+2 y+1=0

Correct answer

C. x+2y+4=0x+2 y+4=0

Step-by-step solution

Equation of a tangent to parabola y2=4xy^{2}=4 x is: y=mx+1my=m x+\frac{1}{m} This line is a tangent to xy=2x y=2 ∴x(mx+1m)=2⇒mx2+1mx−2=0\therefore \quad x\left(m x+\frac{1}{m}\right)=2 \Rightarrow m x^{2}+\frac{1}{m} x-2=0 ∵\because Tangent is common for parabola and hyperbola. ∴D=(1m)2−4⋅m⋅(−2)=0\therefore \quad D=\left(\frac{1}{m}\right)^{2}-4 \cdot m \cdot(-2)=0 1m2+8m=0\frac{1}{m^{2}}+8 m=0 1+8m3=01+8 m^{3}=0 m3=−18⇒m=−12m^{3}=-\frac{1}{8} \Rightarrow m=-\frac{1}{2} ∴\therefore Equation of common tangent: y=−12x−2y=-\frac{1}{2} x-2 ⇒2y=−x−4⇒x+2y+4=0\Rightarrow 2 y=-x-4 \Rightarrow x+2 y+4=0
Practice Hyperbola on Quantrex Academy →

More from Hyperbola

If the eccentricity e of the hyperbola (x^2)/(a^2) - (y^2)/(b^2) = 1 , passing through… JEE Main 2026Let the eccentricity e of a hyperbola satisfy the equation 6e^2 - 11e + 3 = 0 . If the… JEE Main 2026Let H: (x^2)/(a^2)-(y^2)/(b^2)=1 be a hyperbola such that the distance between its foci… JEE Main 2026Let O be the origin, and P and Q be two points on the rectangular hyperbola xy = 12 such… JEE Main 2026For some θ ∈(0, (π)/(2)) , let the eccentricity and the length of the latus rectum of the… JEE Main 2026Let PQ be a chord of the hyperbola x^ 2 4 - y^ 2 b^ 2 =1 , perpendicular to the x -axis… JEE Main 2026Let the domain of the function f(x)= _ 3 _ 5 _ 7 (9 x-x^ 2 -13) be the interval (m, n) .… JEE Main 2026Let P(10,2 15 ) be a point on the hyperbola x^ 2 a^ 2 - y^ 2 ~b^ 2 =1 , whose foci are S… JEE Main 2026If the line α x+2 y=1 , where α ∈ ℝ , does not meet the hyperbola x^ 2 -9 y^ 2 =9 , then… JEE Main 2026Let the foci of a hyperbola coincide with the foci of the ellipse x^ 2 36 + y^ 2 16 =1 .… JEE Main 2026Let e_1 and e_2 be the eccentricities of the ellipse x^2 ~b^2 + y^2 25 =1 and the… JEE Main 2025Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be… JEE Main 2025Consider the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 having one of its focus at P(-3,0) . If… JEE Main 2025Let the sum of the focal distances of the point P(4,3) on the hyperbola H: x^2 a^2 - y^2… JEE Main 2025If the equation of the hyperbola with foci (4,2) and (8,2) is 3 x^2-y^2-α x+β y+γ=0… JEE Main 2025Let the product of the focal distances of the point P(4,2 3 ) on the hyperbola H: x^2 a^2… JEE Main 2025 Full Hyperbola list Hyperbola JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs