1
JEE Main 2017 (Offline)
+4
-1
A hyperbola passes through the point P$$\left( {\sqrt 2 ,\sqrt 3 } \right)$$ and has foci at $$\left( { \pm 2,0} \right)$$. Then the tangent to this hyperbola at P also passes through the point
A
$$\left( {2\sqrt 2 ,3\sqrt 3 } \right)$$
B
$$\left( {\sqrt 3 ,\sqrt 2 } \right)$$
C
$$\left( { - \sqrt 2 , - \sqrt 3 } \right)$$
D
$$\left( {3\sqrt 2 ,2\sqrt 3 } \right)$$
2
JEE Main 2017 (Offline)
+4
-1
The eccentricity of an ellipse whose centre is at the origin is $${1 \over 2}$$. If one of its directrices is x = – 4, then the equation of the normal to it at $$\left( {1,{3 \over 2}} \right)$$ is
A
2y – x = 2
B
4x – 2y = 1
C
4x + 2y = 7
D
x + 2y = 4
3
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
4
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
$$\left( {5,2\sqrt 3 } \right)$$
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