1
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
2
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
3
JEE Main 2016 (Offline)
+4
-1
The eccentricity of the hyperbola whose length of the latus rectum is equal to $$8$$ and the length of its conjugate axis is equal to half of the distance between its foci, is :
A
$${2 \over {\sqrt 3 }}$$
B
$${\sqrt 3 }$$
C
$${{4 \over 3}}$$
D
$${4 \over {\sqrt 3 }}$$
4
JEE Main 2016 (Offline)
+4
-1
Let $$P$$ be the point on the parabola, $${{y^2} = 8x}$$ which is at a minimum distance from the centre $$C$$ of the circle, $${x^2} + {\left( {y + 6} \right)^2} = 1$$. Then the equation of the circle, passing through $$C$$ and having its centre at $$P$$ is:
A
$${{x^2} + {y^2} - {x \over 4} + 2y - 24 = 0}$$
B
$${{x^2} + {y^2} - 4x + 9y + 18 = 0}$$
C
$${{x^2} + {y^2} - 4x + 8y + 12 = 0}$$
D
$${{x^2} + {y^2} - x + 4y - 12 = 0}$$
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