1

### IIT-JEE 2009

MCQ (More than One Correct Answer)
The tangent $$PT$$ and the normal $$PN$$ to the parabola $${y^2} = 4ax$$ at a point $$P$$ on it meet its axis at points $$T$$ and $$N$$, respectively. The locus of the centroid of the triangle $$PTN$$ is a parabola whose
A
vertex is $$\left( {{{2a} \over 3},0} \right)$$
B
directrix is $$x=0$$
C
latus rectum is $${{{2a} \over 3}}$$
D
focus is $$(a, 0)$$
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)
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
$$y = - 30x - 50$$
4

### 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 $$\left( {5\sqrt 3 ,0} \right)$$

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