Conic Sections · JEE Main previous year questions

2005 5 questions

1. Q162005 · 28 Apr 2005 · Shift 1

   An ellipse has $OB$ as semi minor axis, $F$ and $F^{\prime }$ its foci and the angle $FB{F}^{\prime }$ is a right angle. Then the eccentricity of the ellipse is :

   1. A.$\frac{1}{\sqrt{2}}$
   2. B.$\frac{1}{2}$
   3. C.$\frac{1}{4}$
   4. D.$\frac{1}{\sqrt{3}}$
   Show answer

   Answer: A

2. Q172005 · 28 Apr 2005 · Shift 1

   Let $P$ be the point $(1,0)$ and $Q$ a point on the parabola $y^2=8x$. The locus of mid point of $PQ$ is :

   1. A.$y^2-4x+2=0$
   2. B.$y^2+4x+2=0$
   3. C.$x^2+4y+2=0$
   4. D.$x^2-4y+2=0$
   Show answer

   Answer: A

3. Q222005 · 28 Apr 2005 · Shift 1

   Area of the greatest rectangle that can be inscribed in the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

   1. A.$2ab$
   2. B.$ab$
   3. C.$\sqrt{ab}$
   4. D.$\frac{a}{b}$
   Show answer

   Answer: A

4. Q312005 · 28 Apr 2005 · Shift 1

   The parabolas $y^2=4x$ and $x^2=4y$ divide the square region bounded by the lines $x=4,y=4$ and the coordinate axes. If $S_1,S_2,S_3$ are respectively the areas of these parts numbered from top to bottom ; then $S_1:S_2:S_3$ is :

   1. A.$1:2:1$
   2. B.$1:2:3$
   3. C.$2:1:2$
   4. D.$1:1:1$
   Show answer

   Answer: D

5. Q622005 · 28 Apr 2005 · Shift 1

   The locus of a point $P(\alpha ,\beta )$ moving under the condition that the line $y=\alpha x+\beta$ is tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is :

   1. A.an ellipse
   2. B.a circle
   3. C.a parabola
   4. D.a hyperbola
   Show answer

   Answer: D