Conic Sections · JEE Main previous year questions

2022 32 questions

1. Q202022 · 25 Jun 2022 · Shift 2

   If the line $y=4+kx$, $k>0$, is the tangent to the parabola $y=x-x^2$ at the point $\mathrm{P}$ and $\mathrm{V}$ is the vertex of the parabola, then the slope of the line through $\mathrm{P}$ and $\mathrm{V}$ is :

   1. A.$\frac{3}{2}$
   2. B.$\frac{26}{9}$
   3. C.$\frac{5}{2}$
   4. D.$\frac{23}{6}$
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   Answer: C

2. Q302022 · 25 Jun 2022 · Shift 2· Numerical answer

   Let the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be $\frac{5}{4}$. If the equation of the normal at the point $\left(\frac{8}{\sqrt{5}},\frac{12}{5}\right)$ on the hyperbola is $8\sqrt{5}x+\beta y=\lambda$, then $\lambda -\beta$ is equal to ____.

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   Answer: 85

3. Q72022 · 24 Jun 2022 · Shift 2

   A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the point P meets the x-axis at Q. If the y-axis bisects the segment PQ, then C is a parabola with :

   1. A.length of latus rectum 3
   2. B.length of latus rectum 6
   3. C.focus $\left(\frac{4}{3},0\right)$
   4. D.focus $\left(0,\frac{3}{4}\right)$
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   Answer: A

4. Q82022 · 24 Jun 2022 · Shift 2

   Let the maximum area of the triangle that can be inscribed in the ellipse $\frac{x^2}{a^2}+\frac{y^2}{4}=1$, $a>2$, having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the y-axis, be $6\sqrt{3}$. Then the eccentricity of the ellipse is :

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

5. Q262022 · 24 Jun 2022 · Shift 2· Numerical answer

   The area (in sq. units) of the region enclosed between the parabola $y^2=2x$ and the line $x+y=4$ is ____.

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   Answer: 18

6. Q282022 · 24 Jun 2022 · Shift 2· Numerical answer

   Let the hyperbola $H:\frac{x^2}{a^2}-y^2=1$ and the ellipse $E:3x^2+4y^2=12$ be such that the length of latus rectum of H is equal to the length of latus rectum of E. If $e_H$ and $e_E$ are the eccentricities of H and E respectively, then the value of $12\left(e_H^2+e_E^2\right)$ is equal to ____.

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   Answer: 42

7. Q292022 · 24 Jun 2022 · Shift 2· Numerical answer

   Let ${\mathrm{P}}_1$ be a parabola with vertex $(3,2)$ and focus $(4,4)$ and ${\mathrm{P}}_2$ be its mirror image with respect to the line $x+2y=6$. Then the directrix of ${\mathrm{P}}_2$ is $x+2y=$ ____.

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   Answer: 10