WB JEE 2023 | Ellipse Question 14 | Mathematics

WB JEE 2023

MCQ (Single Correct Answer)

-0.25

If the lines joining the focii of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ where $$a > b$$, and an extremity of its minor axis is inclined at an angle 60$$^\circ$$, then the eccentricity of the ellipse is

$${{\sqrt 3 } \over 2}$$

$${1 \over 2}$$

$${{\sqrt 7 } \over 3}$$

$${1 \over {\sqrt 3 }}$$

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

AB is a variable chord of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. If AB subtends a right angle at the origin O, then $${1 \over {O{A^2}}} + {1 \over {O{B^2}}}$$ equals to

$${1 \over {{a^2}}} + {1 \over {{b^2}}}$$

$${1 \over {{a^2}}} - {1 \over {{b^2}}}$$

$${a^2} + {b^2}$$

$${a^2} - {b^2}$$

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

The co-ordinate of a point on the auxiliary circle of the ellipse x² + 2y² = 4 corresponding to the point on the ellipse whose eccentric angle is 60$$^\circ$$ will be

$$(\sqrt 3 ,1)$$

$$(1,\sqrt 3 )$$

(1, 1)

(1, 2)

WB JEE 2021

MCQ (Single Correct Answer)

-0.5

The points of intersection of two ellipses $${x^2} + 2{y^2} - 6x - 12y + 20 = 0$$ and $$2{x^2} + {y^2} - 10x - 6y + 15 = 0$$ lie on a circle. The centre of the circle is

(8, 3)

(8, 1)

$$\left( {{8 \over 3},3} \right)$$

(3, 8)

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