Conic Sections · JEE Main previous year questions

2004 3 questions

1. Q202004 · 24 Apr 2004 · Shift 1

   If $a\ne 0$ and the line $2bx+3cy+4d=0$ passes through the points of intersection of the parabolas $y^2=4ax$ and $x^2=4ay$, then :

   1. A.$d^2+(3b-2c{)}^2=0$
   2. B.$d^2+(3b+2c{)}^2=0$
   3. C.$d^2+(2b-3c{)}^2=0$
   4. D.$d^2+(2b+3c{)}^2=0$
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   Answer: D

2. Q212004 · 24 Apr 2004 · Shift 1

   The eccentricity of an ellipse, with its centre at the origin, is $\frac{1}{2}$. If one of the directrices is $x=4$, then the equation of the ellipse is :

   1. A.$4x^2+3y^2=1$
   2. B.$3x^2+4y^2=12$
   3. C.$4x^2+3y^2=12$
   4. D.$3x^2+4y^2=1$
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   Answer: B

3. Q232004 · 24 Apr 2004 · Shift 1

   A point on the parabola $y^2=18x$ at which the ordinate increases at twice the rate of the abscissa is

   1. A.$\left(\frac{9}{8},\frac{9}{2}\right)$
   2. B.$(2,-4)$
   3. C.$\left(\frac{-9}{8},\frac{9}{2}\right)$
   4. D.$(2,4)$
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   Answer: A