Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Hyperbola

JEE Main · Mathematics · Hyperbola

If equation a x²+2 h x y+b y²+2 g x+2 f y+c=0 represents a...

If equation ax2+2hxy+by2+2gx+2fy+c=0a x²+2 h x y+b y²+2 g x+2 f y+c=0 represents a rectangular hyperbola, then

Options

  1. A(Δ≠\Delta \neq0,  h2<\mathrm{~h}^2<\mathrm{ab}, \mathrm{a}+\mathrm{b} \neq0)
  2. B(Δ≠\Delta \neq0, h2>\mathrm{h}^2>\mathrm{ab}, \mathrm{a}+\mathrm{b}=0)
  3. C(Δ≠\Delta \neq0, h2=\mathrm{h}^2=\mathrm{ab}, \mathrm{a}+\mathrm{b}=0)
  4. D(Δ≠\Delta \neq0,  h2<\mathrm{~h}^2<\mathrm{ab}, \mathrm{a}+\mathrm{b}=0)

Correct answer

B. (Δ≠\Delta \neq0, h2>\mathrm{h}^2>\mathrm{ab}, \mathrm{a}+\mathrm{b}=0)

Step-by-step solution

It is fundamental concept that for equation
ax2+2hxy+by2+2gx+2fy+c=0a x²+2 h x y+b y²+2 g x+2 f y+c=0 to represents a rectangular hyperbola it has to satisfy following condition,
(Δ=abc+\Delta=\mathrm{abc}+2 fgh−af2−\mathrm{fgh}-\mathrm{af}^2-\mathrm{bg}^2-ch2≠0,\mathrm{ch}^2 ≠ 0,\mathrm{h}^2>ab\mathrm{ab}) and (a+b=\mathrm{a}+\mathrm{b}=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 99 Percentile Qs Bank for JEE Main PYQs