1
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
Out of Syllabus
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
2
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
If the tangents drawn to the hyperbola 4y2 = x2 + 1 intersect the co-ordinate axes at the distinct points A and B then the locus of the mid point of AB is :
A
x2 $$-$$ 4y2 + 16x2y2 = 0
B
x2 $$-$$ 4y2 $$-$$ 16x2y2 = 0
C
4x2 $$-$$ y2 + 16x2y2 = 0
D
4x2 $$-$$ y2 $$-$$ 16x2y2 = 0
3
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
The locus of the point of intersection of the straight lines,

tx $$-$$ 2y $$-$$ 3t = 0

x $$-$$ 2ty + 3 = 0 (t $$\in$$ R), is :
A
an ellipse with eccentricity $${2 \over {\sqrt 5 }}$$
B
an ellipse with the length of major axis 6
C
a hyperbola with eccentricity $$\sqrt 5$$
D
a hyperbola with the length of conjugate axis 3
4
JEE Main 2017 (Offline)
+4
-1
Out of Syllabus
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
$$\left( {3\sqrt 2 ,2\sqrt 3 } \right)$$
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