Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2017MathematicsEllipseActual

What is the equation of the ellipse having foci ( 2,0) and the eccentricity 1 4 ?

Options

  1. Ax^2 64 + y^2 60 =1
  2. Bx^2 60 + y^2 64 =1
  3. Cx^2 20 + y^2 24 =1
  4. Dx ^2 24 + y ^2 20 =1

Correct answer

A. x^2 64 + y^2 60 =1

Step-by-step solution

foci: ( 2,0), e = 1 4 c =2, e = 1 4 = c a 2 a = 1 4 a =8 We know, a ^2- b ^2= c ^2 b^2=a^2-c^2=8^2-2^2=64-4=60 Eq q^n of ellipse x^2 a^2 + y^2 b^2 =1 x^2 64 + y^2 60 =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 25(81x^2-144y^2)=11664 coincide (assume p Question: What is the value of p ? 2026Passage: The foci of the ellipse px^2+16y^2=16p and the foci of the hyperbola 25(81x^2-144y^2)=11664 coincide (assume p Question: What is the difference between the eccentricities 2026If any point on an ellipse is (3 , 5 ) , then what is the eccentricity of the ellipse? 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 ellipse, then what is PQ + PR equal to? 2024What is the eccentricity of the ellipse if the angle between the straight lines joining the foci to an extremity of the minor axis is 90^ ? 2024Paragraph: Consider the following for the next two (02) items that follow: P (x, y) is any point on the ellipse x^2+4 y^2=1 . Let E, F be the foci of the ellipse. Question: What is 2023Given that 4 x^2+y^2=9 What is the maximum value of y? 2023Consider the following in respect of the equation x^2 24-k + y^2 k-16 =2 1. The equation represents an ellipse if k =19 . 2. The equation represents a hyperbola if k =12 3. The equ 2023 Full Ellipse list All NDA PYQs