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1

### IIT-JEE 2009

MCQ (More than One Correct Answer)
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
2

### IIT-JEE 2008

MCQ (More than One Correct Answer)
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
$${x^2} + 2\sqrt 3 \,\,y = 3 + \sqrt 3$$
B
$${x^2} - 2\sqrt 3 \,\,y = 3 + \sqrt 3$$
C
$${x^2} + 2\sqrt 3 \,\,y = 3 - \sqrt 3$$
D
$${x^2} - 2\sqrt 3 \,\,y = 3 - \sqrt 3$$
3

### IIT-JEE 2006

MCQ (More than One Correct Answer)
Let a hyperbola passes through the focus of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over {16}} = 1$$. The transverse and conjugate axes of this hyperbola coincide with the major and minor axes of the given ellipse, also the produced of eccentricities of given ellipse and hyperbola is $$1$$, then
A
the equation of hyperbola is $${{{x^2}} \over 9} + {{{y^2}} \over {16}} = 1$$
B
the equation of hyperbola is $${{{x^2}} \over 9} + {{{y^2}} \over {25}} = 1$$
C
focus of hyperbola is $$(5, 0)$$
D
vertex of hyperbola is $$\left( {5\sqrt 3 ,0} \right)$$
4

### IIT-JEE 2006

MCQ (More than One Correct Answer)
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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