Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2011MathematicsEllipseActual

The equation of the ellipse with focus at (( 5,0) ) and (x= 36 5 ) as one directrix is

Options

  1. A( x^2 36 + y^2 25 =1 )
  2. B( x^2 36 + y^2 11 =1 )
  3. C( x^2 25 + y^2 11 =1 )
  4. DNone of these

Correct answer

B. ( x^2 36 + y^2 11 =1 )

Step-by-step solution

We have ae (=5 ) [Since focus is (( ae , 0) )] and ( a e = 36 5 [ . ) since directrix is ( . x = a e ] ) On solving we get ( a =6 ) ( and e = 5 6 b ^2= a ^2 (1- e ^2 )=36 (1- 25 36 )=11 ) Thus, the required equation of the ellipse is ( x^2 36 + y^2 11 =1 )

Practice Ellipse on Quantrex Academy →

More from Ellipse

The eccentricity of the ellipse whose major axis is three times the minor axis is: 2021An ellipse has OB as semi minor axis, F and F ^ its focii and the angle FBF' is a right angle. Then the eccentricity of the ellipse is 2021If x ma + y nb =1 touches the ellipse x² a² + y² b² =1, then 2020If the length of the major axis of the ellipse x 2 a 2 + y 2 b 2 = 1 is three times the length of minor axis, its eccentricity is 2019The locus of the foot of perpendicular drawn from the centre of the ellipse x 2 + 3 y 2 = 6 on any tangent to it is 2019The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x 2 + 9 y 2 = 9 meets its auxiliary circle at the point M . Then, the ar 2018If p and p ' denote the lengths of the perpendicular from a focus and the centre of an ellipse with semi-major axis of length a , respectively, on a tangent to the ellipse and r de 2017The eccentricity of an ellipse, with its centre at the origin, is 1 / 2 . If one of the directrices is x =4 then the equation of the ellipse is: 2015 Full Ellipse list All BITSAT PYQs