Conic Sections · JEE Main previous year questions

2018 6 questions

1. Q172018 · 16 Apr 2018 · Shift 1

   If the length of the latus rectum of an ellipse is 4 units and the distance between a focus and its nearest vertex on the major axis is $\frac{3}{2}$ units, then its eccentricity is :

   1. A.$\frac{1}{2}$
   2. B.$\frac{1}{3}$
   3. C.$\frac{2}{3}$
   4. D.$\frac{1}{9}$
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   Answer: B

2. Q262018 · 16 Apr 2018 · Shift 1

   The differential equation representing the family of ellipse having foci either on the x-axis or on the y-axis, center at the origin and passing through the point (0, 3) is :

   1. A.$xy{y}^{\prime \prime }+x(y^{\prime }{)}^2-y{y}^{\prime }=0$
   2. B.$x+y{y}^{\prime \prime }=0$
   3. C.$xy{y}^{\prime }+y^2-9=0$
   4. D.$xy{y}^{\prime }-y^2+9=0$
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   Answer: D

3. Q182018 · 15 Apr 2018 · Shift 1

   If the tangents drawn to the hyperbola $4y^2=x^2+1$ intersect the co-ordinate axes at the distinct points A and B then the locus of the mid point of AB is :

   1. A.$x^2-4y^2+16x^2{y}^2=0$
   2. B.$x^2-4y^2-16x^2{y}^2=0$
   3. C.$4x^2-y^2+16x^2{y}^2=0$
   4. D.$4x^2-y^2-16x^2{y}^2=0$
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   Answer: B

4. Q252018 · 15 Apr 2018 · Shift 1

   Two parabolas with a common vertex and with axes along x-axis and y-axis, respectively intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is :

   1. A.$4(x+y)+3=0$
   2. B.$3(x+y)+4=0$
   3. C.$8(2x+y)+3=0$
   4. D.$x+2y+3=0$
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   Answer: A

5. Q262018 · 15 Apr 2018 · Shift 1

   If $\beta$ is one of the angles between the normals to the ellipse, $x^2+3y^2=9$ at the points $(3\cos \theta ,\sqrt{3}\sin \theta )$ and $(-3\sin \theta ,\sqrt{3}\cos \theta )$; $\theta \in \left(0,\frac{\pi }{2}\right)$; then $\frac{2\cot \beta }{\sin 2\theta }$ is equal to :

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

6. Q242018 · 8 Apr 2018 · Shift 1

   Tangents are drawn to the hyperbola $4x^2-y^2=36$ at the points P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of $\Delta \mathrm{PTQ}$ is :

   1. A.$36\sqrt{5}$
   2. B.$45\sqrt{5}$
   3. C.$54\sqrt{3}$
   4. D.$60\sqrt{3}$
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   Answer: B