Conic Sections · JEE Main previous year questions

2012 7 questions

1. Q182012 · 26 May 2012 · Shift 1

   The area bounded by the parabola $y^2=4x$ and the line $2x-3y+4=0$, in square unit, is

   1. A.$\frac{2}{5}$
   2. B.$\frac{1}{3}$
   3. C.1
   4. D.$\frac{1}{2}$
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   Answer: B

2. Q252012 · 26 May 2012 · Shift 1

   The chord $PQ$ of the parabola $y^2=x$, where one end $P$ of the chord is at point $(4,-2)$, is perpendicular to the axis of the parabola. Then the slope of the normal at $Q$ is

   1. A.$-4$
   2. B.$-\frac{1}{4}$
   3. C.4
   4. D.$\frac{1}{4}$
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   Answer: A

3. Q262012 · 26 May 2012 · Shift 1

   The normal at $(2,\frac{3}{2})$ to the ellipse, $\frac{x^2}{16}+\frac{y^2}{3}=1$ touches a parabola, whose equation is

   1. A.$y^2=-104x$
   2. B.$y^2=14x$
   3. C.$y^2=26x$
   4. D.$y^2=-14x$
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   Answer: A

4. Q72012 · 12 May 2012 · Shift 1

   The area of triangle formed by the lines joining the vertex of the parabola, $x^2=8y$, to the extremities of its latus rectum is

   1. A.2
   2. B.8
   3. C.1
   4. D.4
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   Answer: B

5. Q242012 · 12 May 2012 · Shift 1

   If $P_1$ and $P_2$ are two points on the ellipse $\frac{x^2}{4}+y^2=1$ at which the tangents are parallel to the chord joining the points $(0,1)$ and $(2,0)$, then the distance between $P_1$ and $P_2$ is

   1. A.$2\sqrt{2}$
   2. B.$\sqrt{5}$
   3. C.$2\sqrt{3}$
   4. D.$\sqrt{10}$
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   Answer: D

6. Q72012 · 7 May 2012 · Shift 1

   If the eccentricity of a hyperbola $\frac{x^2}{9}-\frac{y^2}{b^2}=1$, which passes through $(K,2)$, is $\frac{\sqrt{13}}{3}$, then the value of $K^2$ is

   1. A.18
   2. B.8
   3. C.1
   4. D.2
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   Answer: A

7. Q252012 · 7 May 2012 · Shift 1

   Statement 1: $y=mx-\frac{1}{m}$ is always a tangent to the parabola, $y^2=-4x$ for all non-zero values of $m$. Statement 2: Every tangent to the parabola, $y^2=-4x$ will meet its axis at a point whose abscissa is non-negative.

   1. A.Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
   2. B.Statement 1 is false, Statement 2 is true.
   3. C.Statement 1 is true, Statement 2 is false.
   4. D.Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
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   Answer: D