1
JEE Main 2018 (Online) 16th April Morning Slot
+4
-1
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 $$8\sqrt 2 .$$
2
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
$${1 \over 9}$$
3
JEE Main 2018 (Online) 16th April Morning Slot
+4
-1
Let P be a point on the parabola, x2 = 4y. If the distance of P from the center of the circle, x2 + y2 + 6x + 8 = 0 is minimum, then the equation of the tangent to the parabola at P, is :
A
x + 4y $$-$$ 2 = 0
B
x $$-$$ y + 3 = 0
C
x + y +1 = 0
D
x + 2y = 0
4
JEE Main 2018 (Offline)
+4
-1
Tangents are drawn to the hyperbola 4x2 - y2 = 36 at the points P and Q.

If these tangents intersect at the point T(0, 3) then the area (in sq. units) of $$\Delta$$PTQ is :
A
$$36\sqrt 5$$
B
$$45\sqrt 5$$
C
$$54\sqrt 3$$
D
$$60\sqrt 3$$
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