Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Ellipse

NDA 2010 · Mathematics · Ellipse

If (4,0) and (-4,0) are the foci of an ellipse and the semi-minor...

If (4,0)(4,0) and (−4,0)(-4,0) are the foci of an ellipse and the semi-minor axis is 3 ; then the ellipse passes through which one of the following points?

Options

  1. A(2,0)(2,0)
  2. B(0,5)(0,5)
  3. C(0,0)(0,0)
  4. D(5,0)(5,0)

Correct answer

D. (5,0)(5,0)

Step-by-step solution

 Focus =(±ae,o)b=3, and 2b=6ae=4 But c=4∴c=a2−b2⇒1b=a2−b2 or a2=16+9∴a=5,b=3∴x225+b29=1\begin{aligned} & \text{ Focus }=( \pm a e, o) \\ & b=3, \text{ and } \\ & 2 b=6 \\ & a e=4 \\ & \text{ But } c=4 \\ & \therefore c=\sqrt{a^2-b^2} \\ & \Rightarrow 1 b=a^2-b^2 \text{ or } a^2=16+9 \\ & \therefore a=5, b=3 \\ & \therefore \frac{x^2}{25}+\frac{b^2}{9}=1 \end{aligned} which clearly passes through (5,0)(5,0)
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