1
JEE Main 2018 (Online) 16th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
The differential equation representing the family of ellipse having foci eith on the x-axis or on the $$y$$-axis, center at the origin and passing through the point (0, 3) is :
A
xy y'' + x (y')2 $$-$$ y y' = 0
B
x + y y'' = 0
C
xy y'+ y2 $$-$$ 9 = 0
D
xy y' $$-$$ y2 + 9 = 0
2
JEE Main 2018 (Online) 16th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The locus of the point of intersection of the lines, $$\sqrt 2 x - y + 4\sqrt 2 k = 0$$ and $$\sqrt 2 k\,x + k\,y - 4\sqrt 2 = 0$$ (k is any non-zero real parameter), is :
A
an ellipse whose eccentricity is $${1 \over {\sqrt 3 }}.$$
B
an ellipse with length of its major axis $$8\sqrt 2 .$$
C
a hyperbola whose eccentricity is $$\sqrt 3 .$$
D
a hyperbola with length of its transverse axis $$8\sqrt 2 .$$
3
JEE Main 2018 (Online) 16th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If a circle C, whose radius is 3, touches externally the circle,
$${x^2} + {y^2} + 2x - 4y - 4 = 0$$ at the point (2, 2), then the length of the intercept cut by this circle C, on the x-axis is equal to :
A
$$2\sqrt 5 $$
B
$$3\sqrt 2 $$
C
$$\sqrt 5 $$
D
$$2\sqrt 3 $$
4
JEE Main 2018 (Online) 16th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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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