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Question - 1

The axis of the parabola  \({ y }^{ 2 }-2y+8x-23=0\) is

  • A \(Y=-1\)
  • B \(x=-3\)
  • C \(x= 3\)
  • D \(y= 1\)

Question - 2

\({ 16x }^{ 2 }-3{ y }^{ 2 }-32x-44=0\)represents

  • A an ellipse
  • B a circle
  • C a parabola           
  • D  a hyperbola.

Question - 3

The line   \({ 4x+2y=c }\)    is a tangent  to the parabola \({ y }^{ 2 } = 16x\)  then c is.

  • A -1
  • B -2           
  • C 4
  • D -4

Question - 4

The point of intersection of the tangents \({ t }_{ 1 }=t\quad \) and  \({ t }_{ 2 }=3t\quad \) to the parabola \({ y }^{ 2 }=8x\) is

  • A \(\left( 6{ t }^{ 2 },8t \right) \)
  • B \(\left( 8t,6{ t }^{ 2 } \right) \)
  • C \(\left( { t }^{ 2 },4t \right) \)
  • D \(\left( 4t,{ t }^{ 2 } \right) \)

Question - 5

The length of the latus rectum of the parabola   \({ y }^{ 2 }-4x+4y+8=0\)   is

  • A 8
  • B  6          
  • C 4
  • D 2

Question - 6

The directrix of the parabola  \({ { y }^{ 2 } }=x+4\quad \) is

  • A \(x=\frac { 15 }{ 4 } \)
  • B \(x=-\frac { 15 }{ 4 } \)
  • C \(x=-\frac { 17 }{ 4 } \)
  • D \(x=\frac { 17 }{ 4 } \)

Question - 7

The length of the latus rectum of the parabola whose vertex \(\left( 2,-3 \right) \) and the directrix x=4 is

  • A 2
  • B 4             
  • C 6
  • D 8

Question - 8

The focus of the parabola   \({ x }^{ 2 }=16y\)   is

  • A \(\left( 4,0 \right) \)
  • B \(\left( 0,4 \right) \)
  • C \(\left( -4,0 \right) \)
  • D \(\left( 0,-4 \right) \)

Question - 9

  The vertex of the parabola \({ x }^{ 2 }=8y-1\) is

  • A \(\left( -\frac { 1 }{ 8 } ,0 \right) \)
  • B \(\left( \frac { 1 }{ 8 } ,0 \right) \)
  • C \(\left( 0,\frac { 1 }{ 8 } \right) \)
  • D \(\left( 0,-\frac { 1 }{ 8 } \right) \)

Question - 10

The line   \(2x+3y+9=0\)  touches the parabola  \({ y }^{ 2 }=8x\) at the point

  • A \(\left( 0,-3 \right) \)
  • B \(\left( 2,4 \right) \)
  • C \(\left( -6,\quad \frac { 9 }{ 2 } \right) \)
  • D \(\left( \frac { 9 }{ 2 } ,-6 \right) \)