1
JEE Main 2019 (Online) 9th January Morning Slot
+4
-1 Let $$0 < \theta < {\pi \over 2}$$. If the eccentricity of the

hyperbola $${{{x^2}} \over {{{\cos }^2}\theta }} - {{{y^2}} \over {{{\sin }^2}\theta }}$$ = 1 is greater

than 2, then the length of its latus rectum lies in the interval :
A
(3, $$\infty$$)
B
$$\left( {{3 \over 2},2} \right]$$
C
$$\left( {1,{3 \over 2}} \right]$$
D
$$\left( {2,3} \right]$$
2
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 $$8\sqrt 2 .$$
3
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
$$60\sqrt 3$$
4
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1 A normal to the hyperbola, 4x2 $$-$$ 9y2 = 36 meets the co-ordinate axes $$x$$ and y at A and B, respectively. If the parallelogram OABP (O being the origin) is formed, then the ocus of P is :
A
4x2 + 9y2 = 121
B
9x2 + 4y2 = 169
C
4x2 $$-$$ 9y2 = 121
D
9x2 $$-$$ 4y2 = 169
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