Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Ellipse

NDA 2017 · Mathematics · Ellipse

The equation of the ellipse whose centre is at origin, major axis...

The equation of the ellipse whose centre is at origin, major axis is along x -axis with eccentricity 34andlatusrectum4unitsis\frac{3}{4} and latus rectum 4 units is

Options

  1. Ax21024+7y264=1\frac{\mathrm{x}^2}{1024}+\frac{7 \mathrm{y}^2}{64}=1
  2. B49x21024+7y264=1\frac{49 \mathrm{x}^2}{1024}+\frac{7 \mathrm{y}^2}{64}=1
  3. C7x21024+49y264=1\frac{7 x^2}{1024}+\frac{49 y^2}{64}=1
  4. Dx21024+y264=1\frac{\mathrm{x}^2}{1024}+\frac{\mathrm{y}^2}{64}=1

Correct answer

B. 49x21024+7y264=1\frac{49 \mathrm{x}^2}{1024}+\frac{7 \mathrm{y}^2}{64}=1

Step-by-step solution

Given, b2=2a,c2=(34)2a2=916a2\mathrm{b}^2=2 \mathrm{a}, \mathrm{c}^2=\left(\frac{3}{4}\right)^2 \mathrm{a}^2=\frac{9}{16} \mathrm{a}^2 We know, a2=b2+c2a^2=b^2+c^2 So, a2=2a+916a2⇒16a2=32a+9a2⇒7a2=32a⇒a=327∴b2=647\begin{aligned} a^2= & 2 a+\frac{9}{16} a^2 \Rightarrow 16 a^2=32 a+9 a^2 \Rightarrow 7 a^2=32 a \Rightarrow a=\frac{32}{7} \\ & \therefore b^2=\frac{64}{7}\end{aligned} Equation of ellipse is x2a2+y2b2=1⇒x2(327)2+y2647=1⇒49x21024+7y264=1\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \Rightarrow \frac{x^2}{\left(\frac{32}{7}\right)^2}+\frac{y^2}{\frac{64}{7}}=1 \Rightarrow \frac{49 x^2}{1024}+\frac{7 y^2}{64}=1
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 2024Paragraph: Consider the following for the next two (02) items that follow: P(x, y) is any… NDA 2023Given 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 2018 Full Ellipse list Ellipse JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs