Testbook Logo
Exams SuperCoaching Test Series Skill Academy
More
English
Hindi

Question

Download Solution PDF

The foci of the ellipse 4x2 + 9y2 = 1 are at Q and R. If P(x, y) is any point on the ellipse, then what is PQ + PR equal to?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
Download PDF Attempt Online
View all NDA Papers >
  1. 2
  2. 1
  3. 2/3
  4. 1/3

Answer (Detailed Solution Below)

Option 2 : 1
Free Tests
View all Free tests >
Free
NDA 01/2025: English Subject Test
5.3 K Users
30 Questions 120 Marks 30 Mins
Start Now

Detailed Solution

Download Solution PDF

Explanation:

Given:

4x2 + 9y2 = 1 

Here a = 1/2 and b = 1/3

Now 

e = \(\sqrt{1-\frac{b^2}{a^2}} = \frac{\sqrt5}{3}\)

foci = (±ae, 0)

= ( ± \((\frac{1}{2}\frac{\sqrt5}{3},0)\)

= (± \(\frac{\sqrt5}{6},0\))

Thus, P(x, y) is any point on the ellipse

⇒ PQ + PR = 2a = 2× 1/2 = 1

∴ Option (b) is correct.

Download Solution PDF
Latest NDA Updates

Last updated on May 30, 2025

->UPSC has released UPSC NDA 2 Notification on 28th May 2025 announcing the NDA 2 vacancies.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced for cycle 2. The written examination will be held on 14th September 2025.

-> Earlier, the UPSC NDA 1 Exam Result has been released on the official website.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

‹‹ Previous Ques
Next Ques ››

More Ellipse Questions

Q1.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
Q2.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
Q3.Find the points on the curve \(\frac{x^{2}}{9}+\frac{y^{2}}{16}=1\), the tangents at which are parallel to x-axis.
Q4.The area of an ellipse with semi major axis 'a' and semi minor axis 'b' is ______
Q5.The area (in square units) of the triangle formed by the two ends of a latus rectum and a focus of the ellipse \(\frac{x^2}{16}+\frac{y^2}{4}=1\), is:
Q6.If e is the eccentricity of the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) (a < b), then
Q7.The equation of the ellipse whose focus is (1, –1), the directrix the line x – y – 3 = 0 and eccentricity \(\frac{1}{2}\) is 
Q8. The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which passes through the points (–3, 1) and (2, –2) is
Q9.The centre of an ellipse is at (0, 0), major axis is on the y-axis. If the ellipse passes through (3, 2) and (1, 6), then what is its eccentricity ?
Q10.The point (a cos θ + b sin θ, a sin θ - b cos θ) lies on

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

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
SuperCoaching
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 gold apk download teen patti real money app online teen patti real money teen patti real