1
IIT-JEE 2009 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
The normal at a point $$P$$ on the ellipse $${x^2} + 4{y^2} = 16$$ meets the $$x$$- axis $$Q$$. If $$M$$ is the mid point of the line segment $$PQ$$, then the locus of $$M$$ intersects the latus rectums of the given ellipse at the points
2
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-0
Match the conics in Column I with the statements/expressions in Column II :
Column I | Column II | ||
---|---|---|---|
(A) | Circle | (P) | The locus of the point ($$h,k$$) for which the line $$hx+ky=1$$ touches the circle $$x^2+y^2=4$$. |
(B) | Parabola | (Q) | Points z in the complex plane satisfying $$|z+2|-|z-2|=\pm3$$. |
(C) | Ellipse | (R) | Points of the conic have parametric representation $$x = \sqrt 3 \left( {{{1 - {t^2}} \over {1 + {t^2}}}} \right),y = {{2t} \over {1 + {t^2}}}$$ |
(D) | Hyperbola | (S) | The eccentricity of the conic lies in the interval $$1 \le x \le \infty $$. |
(T) | Points z in the complex plane satisfying $${\mathop{\rm Re}\nolimits} {(z + 1)^2} = |z{|^2} + 1$$. |
3
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
The line passing through the extremity $$A$$ of the major axis and extremity $$B$$ of the minor axis of the ellipse $${x^2} + 9{y^2} = 9$$ meets its auxiliary circle at the point $$M$$. Then the area of the triangle with vertices at $$A$$, $$M$$ and the origin $$O$$ is
4
IIT-JEE 2008 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Consider the two curves $${C_1}:{y^2} = 4x,\,{C_2}:{x^2} + {y^2} - 6x + 1 = 0$$. Then,
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