English
Hindi

Question

Download Solution PDF

The equations of the ellipse whose vertices are (±10, 0) and foci at (±9, 0) is

Answer (Detailed Solution Below)

Option 4 :
Free Tests
View all Free tests >
Free
UPSC NDA 01/2025 General Ability Full (GAT) Full Mock Test
150 Qs. 600 Marks 150 Mins
Start Now

Detailed Solution

Download Solution PDF

Since vertices of an ellipse are (±a, 0) and foci are (±ae, 0)

∴ a = 10 and ae = 9

Where e is the eccentricity of ellipse,

We know,

Hence, required equation of ellipse is

Download Solution PDF
Latest NDA Updates

Last updated on Jul 8, 2025

->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.

->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.

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

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

-> 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. 

Exams Tests Super Practice

More Ellipse Questions

Q1.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?
Q2.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
Q3.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
Q4.Find the points on the curve \(\frac{x^{2}}{9}+\frac{y^{2}}{16}=1\), the tangents at which are parallel to x-axis.
Q5.The area of an ellipse with semi major axis 'a' and semi minor axis 'b' is ______
Q6.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:
Q7.If e is the eccentricity of the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) (a < b), then
Q8.The equation of the ellipse whose focus is (1, –1), the directrix the line x – y – 3 = 0 and eccentricity \(\frac{1}{2}\) is 
Q9. 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
Q10.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 ?

More Parabola, Ellipse and Hyperbola Questions

Q1.Consider the points P(4k, 4k) and Q(4k, -4k) lying on the parabola y2 = 4kx. If the vertex is A, then what is ∠PAQ equal to?
Q2.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?
Q3.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
Q4.If y = mx + 4 is a tangent to both the parabolas, y2 = 4x and x2 = 2by, then b is equal to
Q5.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
Q6.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 :
Q7.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
Q8. 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 
Q9.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 ?
Q10.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  
Suggested Test Series
View All >
Current Affairs (CA) 2025 Mega Pack for SSC/Railways/State Exam Mock Test
431 Total Tests with 1 Free Tests
Start Free Test
Current Affairs (CA) 2024 Mega Pack for SSC/Railways/State Exam Mock Test
427 Total Tests with   1 Free Tests
Start Free Test

NDA Important Links

ResultAdmit CardApplication FormEligibilitySalarySyllabus

More Mathematics Questions

Q1.If cosec θ + cot θ = p, then \(\rm\frac{p^2-1}{p^2+1}\) equal:
Q2.In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
Q3.Three perfect dice D1, D2 and D3 and are rolled. Let x, represent the numbers on D1, D2 and D3 respectively. What is the number of possible outcomes such that x < y < z?
Q4.Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?
Q5.The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?
Q6.Two perfect dice are thrown. What C is the probability that the sum of the numbers on the faces is neither 9 nor 10?
Q7.Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
Q8.A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?  
Q9.The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?
Q10.Let \(\rm \Sigma_{i=1}^9x_i^2=885\) If M is the mean and σ is the standard deviation of  x1, x2, x3.....x9 then what is the value of M2 + σ2?
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
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
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： all teen patti master teen patti noble teen patti jodi teen patti 500 bonus