Testbook Logo
Exams SuperCoaching Test Series Skill Academy
More
English
Hindi

Question

Download Solution PDF

The asymptotes of the curve x2y2 = a2 (x2 + y2)

This question was previously asked in
AAI ATC Junior Executive 2016 Official Paper (Shift 2)
Download PDF Attempt Online
View all AAI JE ATC Papers >
  1. Forms a square of side a/2
  2. Forms a square of side a
  3. Forms a square of side 3a/2
  4. Forms a square of side 2a

Answer (Detailed Solution Below)

Option 4 : Forms a square of side 2a
Free Tests
View all Free tests >
Free
AAI ATC JE Physics Mock Test
7.1 K Users
15 Questions 15 Marks 15 Mins
Start Now

Detailed Solution

Download Solution PDF

x2y2 = a2(x2 + y2)

x2 (y2 - a2) - (y2 a2) = 0

Highest power of x is x2

Co-efficient of x2 is y - a2

The asymptotes parallel to the x-axis are given by:

y2 - a2 = 0

y = ± a

Highest power of y is y2 and its co-efficient is x2 - a2

The asymptotes parallel to the y-axis are given by:

x2 - a2 = 0

x = ± a

ATC Previous Year Quiestions Maths.docx 3

These lines form a square with side 2a.

Download Solution PDF
Latest AAI JE ATC Updates

Last updated on Jun 19, 2025

-> The AAI ATC Exam 2025 will be conducted on July 14, 2025 for Junior Executive.. 

-> AAI JE ATC recruitment 2025 application form has been released at the official website. The last date to apply for AAI ATC recruitment 2025 is May 24, 2025. 

-> AAI JE ATC 2025 notification is released on April 4, 2025, along with the details of application dates, eligibility, and selection process.

-> A total number of 309 vacancies are announced for the AAI JE ATC 2025 recruitment.

-> This exam is going to be conducted for the post of Junior Executive (Air Traffic Control) in the Airports Authority of India (AAI).

-> The Selection of the candidates is based on the Computer-Based Test, Voice Test and Test for consumption of Psychoactive Substances.

-> The AAI JE ATC Salary 2025 will be in the pay scale of Rs 40,000-3%-1,40,000 (E-1).

-> Candidates can check the AAI JE ATC Previous Year Papers to check the difficulty level of the exam.

-> Applicants can also attend the AAI JE ATC Test Series which helps in the preparation.

More Hyperbola Questions

Q1.Consider a hyperbola H having centre at the origin and foci and the x - axis. Let C1 be the circle touching the hyperbola H and having the centre at the origin. Let C2 be the circle touching the hyperbola H at its vertex and having the centre at one of its foci. If areas (in sq. units) of C1 and C2 are 36π and 4π, respectively, then the length (in units) of latus rectum of H is  
Q2.If e1 and e2 are eccentricities of the hyperbolas \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) and \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=-1\) respectively, then \(\frac{1}{e_{1}^{2}}+\frac{1}{e_{2}^{2}}\) is
Q3.For the curve x2y2 = a2(x2 + y2), the asymptotes parallel to the coordinates axes are
Q4.Equation of the hyperbola with eccentricty \(\frac{3}{2}\) and foci at (± 2, 0) is
Q5.The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half of the distance between the foci is
Q6.The length of the transverse axis along x-axis with centre at origin of a hyperbola is 7 and it passes through the point (5, –2). The equation of the hyperbola is
Q7.One of the asymptote of curve x3 + 3x2y - 4y3 - x + y + 3 = 0 is
Q8.For the hyperbola 9x2 − 16y2 = 144, the true statement is :
Q9.Let e and e' be the eccentricities of the hyperbola and its conjugate hyperbola, then true statement is
Q10.For what values of k, the line y = kx + 2 will be tangent to the conic 4x2 - 9y2 = 36

More Parabola, Ellipse and Hyperbola Questions

Q1.The locus of the mid-point of the line segment joining the focus of the parabola y2 = 4ax to a moving point of the parabola, is another parabola whose directrix is
Q2.If y = mx + 4 is a tangent to both the parabolas, y2 = 4x and x2 = 2by, then b is equal to
Q3.If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is
Q4.If P is a point on the parabola y = x2 + 4 which is closest to the straight line y = 4x − 1, then the co-ordinates of P are :
Q5.Let the line 2x + 3y – k = 0, k > 0, intersect the x-axis and y-axis at the points A and B, respectively. If the equation of the circle having the line segment AB as a diameter is x2 + y2 – 3x – 2y = 0 and the length of the latus rectum of the ellipse x2 + 9y2 = k2 is \(\frac{m}{n}\) , where m and n are coprime, then 2m + n is equal to
Q6. Let R be the focus of the parabola y2 = 20x and the line y = mx + c intersect the parabola at two points P and Q. Let the point G(10, 10) be the centroid of the triangle PQR. If c – m = 6, then (PQ)2 is 
Q7.Let PQ be a chord of the parabola y2 = 12x and the midpoint of PQ be at (4, 1). Then, which of the following point lies on the line passing through the points P and Q ?
Q8.Consider a hyperbola H having centre at the origin and foci and the x - axis. Let C1 be the circle touching the hyperbola H and having the centre at the origin. Let C2 be the circle touching the hyperbola H at its vertex and having the centre at one of its foci. If areas (in sq. units) of C1 and C2 are 36π and 4π, respectively, then the length (in units) of latus rectum of H is  
Q9.What is the length of the latus rectum of the curve \(\rm x = \frac{y^2}{21}\) ?
Q10.The equation of the normal to the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) at the point (a cos θ, b sin θ) is
Crack AAI ATC Selection Kit with
India's Super Teachers
Explore Supercoaching For FREE
Suggested Test Series
View All >
AAI ATC Junior Executive 2025 Mock Test Series
201 Total Tests with 2 Free Tests
Start Free Test
Vocabulary Master for All Government Exams Mock Test
309 Total Tests with   1 Free Tests
Start Free Test
Suggested Exams
Exam-Logo
AAI JE ATC

AAI JE ATC Important Links

More Mathematics Questions

Q1.log10 10000 = _______?
Q2.Consider a system equation \(2x+y-z=0\), \(4x - py + 4z = 4\) and \(x-y+z=q\) where \(p, q \in I\) and \(p, q \in [1, 10]\), then identify the correct statement(s).   List-I List-II (I) Number of ordered pairs \((p, q)\) for which system of equation has unique solution is (P) 1 (II) Number of ordered pairs \((p, q)\) for which system of equation has no solution is (Q) 9 (III) Number of ordered pairs \((p, q)\) for which system of equation has infinite solution is (R) 91 (IV) Number of ordered pairs \((p, q)\) for which system of equation has atleast one solution is (S) 90
Q3.Match List I with List II:   List - I List - II (I) The number of solutions of the equation\((1 - \cos 2x)(\cos 2x + \cot^2 x) = 0\) where \(0 \le x \le 2\pi\) is (P) 4 (II) \(\tan 81^\circ - \tan 63^\circ - \tan 27^\circ + \tan 9^\circ\) equals (Q) 3 (III) The number of solutions of (x, y), which satisfy |y| = sin x and y = cos-1(cos x), where -2π ≤ x ≤ 2π is (R) 2 (IV) For the equation \(\cos^{-1}x + \cos^{-1}2x + \pi = 0\), the number of real solutions is (S) 1     (T) 0  
Q4.If Σn = 36, find n
Q5.If log 2 = 0.2614, log 3 = 0.3521, log 6 = ?
Q6.The growth model for a population is Nt = N0ert where Nt is the population at time t, N0 is the initial population and r is the per capita growth rate. How long does it take for the population numbers to double?
Q7.Suppose that the growth rate of the number of individuals (N) in a population in an environment with a carrying capacity K is modelled as \(\frac{d N}{d t}=r N \frac{K-N}{K}\) where r is the per capita growth rate and t is time; r and K are positive constants. At which of the following values of N will the population growth rate be the maximum?
Q8.The shadow of a vertical pole, formed due to a nearby lamp which is at a height of 12 m, measures 4 m. If the lamp is moved horizontally 2 m further away from the pole, the length of the shadow measures 8 m. What is the height (in m) of the pole?
Q9.A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Out of these 16 number of cards, two cards are drawn at random. Find the probability that at least one of them is an ace :
Q10.If the equations 2x2 + kx - 5 = 0 and x2 - 3x - 4 = 0 have one root common, then find the value of k.
Important Exams
Super Coaching
Exams
Test Series
Previous Year Papers
Objective Questions
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
[email protected]
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Our Apps
Follow us on
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Get Free Access Now
Hot Links： teen patti all game teen patti 50 bonus yono teen patti teen patti club apk rummy teen patti