1
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?
A
$$\left( {4\sqrt 2 ,2\sqrt 3 } \right)$$
B
$$\left( {4\sqrt 3 ,2\sqrt 3 } \right)$$
C
$$\left( {4\sqrt 3 ,2\sqrt 2 } \right)$$
D
$$\left( {4\sqrt 2 ,2\sqrt 2 } \right)$$
2
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
Out of Syllabus
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 :
A
$${{{x^2}} \over 2} + {{{y^2}} \over 4} = 1$$
B
$${1 \over {2{x^2}}} + {1 \over {4{y^2}}} = 1$$
C
$${1 \over {4{x^2}}} + {1 \over {2{y^2}}} = 1$$
D
$${{{x^2}} \over 4} + {{{y^2}} \over 2} = 1$$
3
JEE Main 2019 (Online) 10th January Evening Slot
+4
-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 :
A
an ellipse whose eccentricity is $${1 \over {\sqrt {r + 1} }},$$ where r > 1
B
an ellipse whose eccentricity is $${2 \over {\sqrt {r + 1} }},$$ where 0 < r < 1
C
an ellipse whose eccentricity is $${2 \over {\sqrt {r - 1} }},$$ where 0 < r < 1
D
an ellipse whose eccentricity is $$\sqrt {{2 \over {r + 1}}}$$, where r > 1
4
JEE Main 2018 (Online) 16th April Morning Slot
+4
-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 :
A
$${1 \over 2}$$
B
$${1 \over 3}$$
C
$${2 \over 3}$$
D
$${1 \over 9}$$
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