JEE Main 2019 (Online) 11th January Morning Slot | Ellipse Question 67 | Mathematics

If tangents are drawn to the ellipse x2 + 2y² = 2 at all points on the ellipse other than its four vertices then the mid points of the tangents intercepted between the coordinate axes lie on the curve :

$${{{x^2}} \over 2} + {{{y^2}} \over 4} = 1$$

$${1 \over {2{x^2}}} + {1 \over {4{y^2}}} = 1$$

$${1 \over {4{x^2}}} + {1 \over {2{y^2}}} = 1$$

$${{{x^2}} \over 4} + {{{y^2}} \over 2} = 1$$

JEE Main 2019 (Online) 10th January Evening Slot

MCQ (Single Correct Answer)

-1

Let S = $$\left\{ {\left( {x,y} \right) \in {R^2}:{{{y^2}} \over {1 + r}} - {{{x^2}} \over {1 - r}}} \right\};r \ne \pm 1.$$ Then S represents :

an ellipse whose eccentricity is $${1 \over {\sqrt {r + 1} }},$$ where r > 1

an ellipse whose eccentricity is $${2 \over {\sqrt {r + 1} }},$$ where 0 < r < 1

an ellipse whose eccentricity is $${2 \over {\sqrt {r - 1} }},$$ where 0 < r < 1

an ellipse whose eccentricity is $$\sqrt {{2 \over {r + 1}}}$$, where r > 1

JEE Main 2018 (Online) 16th April Morning Slot

MCQ (Single Correct Answer)

-1

If the length of the latus rectum of an ellipse is 4 units and the distance between a focus an its nearest vertex on the major axis is $${3 \over 2}$$ units, then its eccentricity is :

$${1 \over 2}$$

$${1 \over 3}$$

$${2 \over 3}$$

$${1 \over 9}$$

JEE Main 2017 (Online) 9th April Morning Slot

MCQ (Single Correct Answer)

-1

The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points (4, −1) and (−2, 2) is :

$${1 \over 2}$$

$${2 \over {\sqrt 5 }}$$

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

$${{\sqrt 3 } \over 4}$$