Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Ellipse

NDA 2023 · Mathematics · Ellipse

Paragraph: Consider the following for the next two (02) items that...

Paragraph: Consider the following for the next two (02) items that follow: P(x,y)\mathrm{P}(x, y) is any point on the ellipse x2+4y2=1x^2+4 y^2=1. Let E,FE, F be the foci of the ellipse.
Question: What is PE+PFP E+P F equal to?

Options

  1. A11
  2. B22
  3. C33
  4. D44

Correct answer

B. 22

Step-by-step solution

x2+4y2=1x21+y2(14)=1a2=1,b2=14⇒a=1,b=12∵Ex^2+4 y^2=1\frac{x^2}{1}+\frac{y^2}{\left(\frac{1}{4}\right)}=1a^2=1, b^2=\frac{1}{4}\Rightarrow a=1, b=\frac{1}{2}\because \quad E and FF are foci ∴PE+PF=2a=\therefore \quad P E+P F=2 a= major axis =2(1)=2=2(1)=2.
Practice Ellipse on Quantrex Academy →

More from Ellipse

Passage: The foci of the ellipse px^2+16y^2=16p and the foci of the hyperbola… NDA 2026Passage: The foci of the ellipse px^2+16y^2=16p and the foci of the hyperbola… NDA 2026If any point on an ellipse is (3 α, 5 α) , then what is the eccentricity of the ellipse? NDA 2025The foci of the ellipse 4 x^2+9 y^2=1 are at Q and R. If P(x, y) is any point on the… NDA 2024What is the eccentricity of the ellipse if the angle between the straight lines joining… NDA 2024Given that 4 x^2+y^2=9 What is the maximum value of y? NDA 2023Consider the following in respect of the equation (x^2)/(24-k)+(y^2)/(k-16)=2 1. The… NDA 2023Paragraph: Consider the following for the next two (02) items that follow: P(x, y) is any… NDA 2023The centre of an ellipse is at (0,0) , major axis is on the y -axis. If the ellipse… NDA 2022What is the distance between the foci of the ellipse x^2+2 y^2=1 ? NDA 2022Consider the following with regard to eccentricity (e) of a conic section : 1. e=0 for… NDA 2021Let P(x, y) be any point on the ellipse 25 x^2+16 y^2=400 . If Q(0,3) and R(0,-3) are two… NDA 2020If the angle between the lines joining the end points of minor axis of the ellipse… NDA 2019The sum of the focal distances of a point on an ellipse is constant and equal to the NDA 2019What is the equation of the ellipse whose vertices are ( ± 5,0) and foci are at ( ± 4,0) ? NDA 2018The second degree equation x^2+4 y-2 x-4 y+2=0 represents NDA 2018 Full Ellipse list Ellipse JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs