1
IIT-JEE 2009 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
An ellipse intersects the hyperbola $$2{x^2} - 2{y^2} = 1$$ orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes then
A
equation of ellipse is $${x^2} + 2{y^2} = 2$$
B
the foci of ellipse are $$\left( { \pm 1,0} \right)$$
C
equation of ellipse is $${x^2} + 2{y^2} = 4$$
D
the foci of ellipse are $$\left( { \pm \sqrt 2 ,0} \right)$$
2
IIT-JEE 2009 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
In a triangle $$ABC$$ with fixed base $$BC$$, the vertex $$A$$ moves such that $$$\cos \,B + \cos \,C = 4{\sin ^2}{A \over 2}.$$$

If $$a, b$$ and $$c$$ denote the lengths of the sides of the triangle opposite to the angles $$A, B$$ and $$C$$, respectively, then

A
$$b+c=4a$$
B
$$b+c=2a$$
C
locus of point $$A$$ is an ellipse
D
locus of point $$A$$ is a pair of straight lines
3
IIT-JEE 2008 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let $$P\left( {{x_1},{y_1}} \right)$$ and $$Q\left( {{x_2},{y_2}} \right),{y_1} < 0,{y_2} < 0,$$ be the end points of the latus rectum of the ellipse $${x^2} + 4{y^2} = 4.$$ The equations of parabolas with latus rectum $$PQ$$ are :
A
$${x^2} + 2\sqrt 3y = 3 + \sqrt 3 $$
B
$${x^2} - 2\sqrt 3y = 3 + \sqrt 3 $$
C
$${x^2} + 2\sqrt 3y = 3 - \sqrt 3 $$
D
$${x^2} - 2\sqrt 3 y = 3 - \sqrt 3 $$
4
IIT-JEE 2006
MCQ (More than One Correct Answer)
+5
-1.25
The equations of the common tangents to the parabola $$y = {x^2}$$ and $$y = - {\left( {x - 2} \right)^2}$$ is/are
A
$$y = 4\left( {x - 1} \right)$$
B
$$y=0$$
C
$$y = - 4\left( {x - 1} \right)$$
D
$$y = - 30x - 50$$
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