Mathematics - Coordinate Geometry - II

Question - 1

The equation of the parabola having vertex at(0,1) and the focus at(0,0), is

  • A \(x^2=4(y-1)\)
  • B \(x^2=-4(y-1)\)
  • C \(x^2=4(y+1)\)
  • D \(x^2=-4(y+1)\)

Question - 2

The equation of the parabola having vertex at(a,0) and focus at (a,0) is

  • A y2=4(a'-a)x
  • B y2=4(a'-a)(x-a')
  • C y2=4(a'-a)(x-a)
  • D None of these

Question - 3

The equation of parabola whose focus is(-8,-2) and the directrix is 2x-y-9=0

  • A \(x^2-4xy+4y^2+116x+2y+259=0\)
  • B \(x^2+4xy+y^2+116x+2y+259=0\)
  • C \(x^2+4xy+4y^2-116x+2y+259=0\)
  • D \(x^2-4xy+4y^2+116x-2y+259=0\)

Question - 4

The coordinates of the vertex and focus of the parabola \(y^2-8y-x+19=0 \)are respectively

  • A \(_{ }(3,4),\left( \frac { 13 }{ 4 } ,4 \right) \)
  • B \(_{ }(-3,-4),\left( \frac { 13 }{ 4 } ,4 \right) \)
  • C \(_{ }(3,4),\left( \frac { -13 }{ 4 } ,-4 \right) \)
  • D None of these

Question - 5

The equation of the matrix of the parabola\(y^2+4y+4x+2=0\) is

  • A x=-1
  • B x=1
  • C \(x=-\frac { 3 }{ 2 } \)
  • D \(x=\frac { 3 }{ 2 } \)

Question - 6

If y1,y2,y3 are the ordinates of the verticles of triangle inscribed in parabola y2=4ax, then area of the triangle, is

  • A \(\frac { 1 }{ 2a } |(y1-y)(y2-y3)(y3-y1)|\)
  • B \(\frac { 1 }{ 4a } |(y1-y)(y2-y3)(y3-y1)|\)
  • C \(\frac { 1 }{ 8a } |(y1-y)(y2-y3)(y3-y1)|\)
  • D \(\frac { 1 }{ 16a } |(y1-y)(y2-y3)(y3-y1)|\)

Question - 7

The curved is represented by the parametric equations x=t2+t+1,y=t2-t+1 is

  • A a pair of straight lines
  • B a circle
  • C a parabola
  • D an ellipse

Question - 8

If the line x-1=0,is the directrix of the parabola y2-kx+8=0,then one of the value of k is

  • A \(1\over8\)
  • B 8
  • C \(1\over4\)
  • D 4

Question - 9

If the vertex of a parabola is(-5,0) and directrix of the line x+3=0 then equation of the parabola,is

  • A y2=4x+16
  • B y2=-4x+16
  • C y2=4x-16
  • D None of these

Question - 10

If lengths of the focal chord segments of the parabola y2=4ax are l1 and l2,then length of the latus rectrum is

  • A \(l1+l2\over2\)
  • B \(4 l1l2\over l1+l2\)
  • C \(2 l1l2\over l1+l2\)
  • D \(\sqrt { l1l2 } \)
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