JEE Main & Advanced Mathematics Conic Sections Question Bank

done Conic section - General Total Questions - 7

• question_answer1)
  The centre of the conic represented by the equation \[2{{x}^{2}}-72xy+23{{y}^{2}}-4x-28y-48=0\] is
  A)
             \[\left( \frac{11}{15},\ \frac{2}{25} \right)\]                done clear
  B)
             \[\left( \frac{2}{25},\ \frac{11}{25} \right)\] done clear
  C)
             \[\left( \frac{11}{15},\ -\frac{2}{25} \right)\]               done clear
  D)
             \[\left( -\frac{11}{25},\ -\frac{2}{25} \right)\] done clear
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• question_answer2)
  The centre of \[14{{x}^{2}}-4xy+11{{y}^{2}}-44x-58y+71=0\] [BIT Ranchi 1986]
  A)
             (2, 3)                                         done clear
  B)
             (2, ? 3) done clear
  C)
             (? 2, 3)                                     done clear
  D)
             (? 2, ? 3) done clear
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• question_answer3)
  The equation of the conic with focus at (1, ?1), directrix along \[x-y+1=0\] and with eccentricity \[\sqrt{2}\] is [EAMCET 1994]
  A)
             \[{{x}^{2}}-{{y}^{2}}=1\]  done clear
  B)
             \[xy=1\] done clear
  C)
             \[2xy-4x+4y+1=0\]             done clear
  D)
             \[2xy+4x-4y-1=0\] done clear
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• question_answer4)
  If a point \[(x,\ y)\equiv (\tan \theta +\sin \theta ,\ \tan \theta -\sin \theta )\], then locus of (x, y) is      [EAMCET 2002]
  A)
             \[{{({{x}^{2}}y)}^{2/3}}+{{(x{{y}^{2}})}^{2/3}}=1\]   done clear
  B)
             \[{{x}^{2}}-{{y}^{2}}=4xy\] done clear
  C)
             \[{{({{x}^{2}}-{{y}^{2}})}^{2}}=16xy\]                             done clear
  D)
             \[{{x}^{2}}-{{y}^{2}}=6xy\] done clear
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• question_answer5)
  Equation\[\sqrt{{{(x-2)}^{2}}+{{y}^{2}}}+\sqrt{{{(x+2)}^{2}}+{{y}^{2}}}=4\]represents  [Orissa JEE 2004]
  A)
             Parabola                                 done clear
  B)
             Ellipse done clear
  C)
             Circle                                        done clear
  D)
             Pair of straight lines done clear
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• question_answer6)
  Angle of intersection of the curves \[r=\sin \theta +\cos \theta \] and \[r=2\sin \theta \] is equal to        [UPSEAT 2004]
  A)
             \[\frac{\pi }{2}\]                  done clear
  B)
             \[\frac{\pi }{3}\] done clear
  C)
             \[\frac{\pi }{4}\]                  done clear
  D)
             None of these done clear
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• question_answer7)
  The equation \[{{y}^{2}}-{{x}^{2}}+2x-1=0\] represents  [UPSEAT 2004]
  A)
             A hyperbola                          done clear
  B)
             An ellipse done clear
  C)
             A pair of straight lines       done clear
  D)
             A rectangular hyperbola done clear
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