1
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
P and Q are two distinct points on the parabola, y2 = 4x, with parameters t and t1 respectively. If the normal at P passes through Q, then the minimum value of $$t_1^2$$ is :
A
2
B
4
C
6
D
8
2
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
A hyperbola whose transverse axis is along the major axis of the conic, $${{{x^2}} \over 3} + {{{y^2}} \over 4} = 4$$ and has vertices at the foci of this conic. If the eccentricity of the hyperbola is $${3 \over 2},$$ then which of the following points does NOT lie on it ?
A
(0, 2)
B
$$\left( {\sqrt 5 ,2\sqrt 2 } \right)$$
C
$$\left( {\sqrt {10} ,2\sqrt 3 } \right)$$
D
$$\left( {5,2\sqrt 3 } \right)$$
3
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1
If the tangent at a point on the ellipse $${{{x^2}} \over {27}} + {{{y^2}} \over 3} = 1$$ meets the coordinate axes at A and B, and O is the origin, then the minimum area (in sq. units) of the triangle OAB is :
A
$${9 \over 2}$$
B
$$3\sqrt 3$$
C
$$9\sqrt 3$$
D
9
4
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1
Let a and b respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation 9e2 − 18e + 5 = 0. If S(5, 0) is a focus and 5x = 9 is the corresponding directrix of this hyperbola, then a2 − b2 is equal to :
A
7
B
$$-$$ 7
C
5
D
$$-$$ 5
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