JEE Main 2020 (Online) 7th January Evening Slot | Ellipse Question 74 | Mathematics

If 3x + 4y = 12$$\sqrt 2 $$ is a tangent to the ellipse
$${{{x^2}} \over {{a^2}}} + {{{y^2}} \over 9} = 1$$ for some $$a$$ $$ \in $$ R, then the distance between the foci of the ellipse is :

$$2\sqrt 5 $$

$$2\sqrt 7 $$

$$2\sqrt 2 $$

JEE Main 2020 (Online) 7th January Morning Slot

MCQ (Single Correct Answer)

-1

If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is :

$$\sqrt 3 $$

$$3\sqrt 2 $$

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

$$2\sqrt 3 $$

JEE Main 2019 (Online) 12th April Evening Slot

MCQ (Single Correct Answer)

-1

An ellipse, with foci at (0, 2) and (0, –2) and minor axis of length 4, passes through which of the following points?

$$\left( {2,\sqrt 2 } \right)$$

$$\left( {2,2\sqrt 2 } \right)$$

$$\left( {\sqrt 2 ,2} \right)$$

$$\left( {1,2\sqrt 2 } \right)$$

JEE Main 2019 (Online) 12th April Morning Slot

MCQ (Single Correct Answer)

-1

Out of Syllabus

If the normal to the ellipse 3x² + 4y² = 12 at a point P on it is parallel to the line, 2x + y = 4 and the tangent to the ellipse at P passes through Q(4,4) then PQ is equal to :

$${{\sqrt {61} } \over 2}$$

$${{\sqrt {221} } \over 2}$$

$${{\sqrt {157} } \over 2}$$

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

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