JEE Maths - Parabola

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Question - 1

The circle x2 + y2 = 5 meets the parabola y2 = 4x at P and Q, then find the length of PQ______

  • A
  • B
  • C
  • D

Question - 2

If P( at12 , 2at1) and Q(at22 , 2at2) are two variable points on the curve y2 = 4ax and PQ subtends a right angle at the vertex then find the value of t1,t2__________

  • A 2
  • B -2
  • C -4
  • D 4

Question - 3

If one end of a focal chord of parabola y2 = 16x is (1, - 4). Then find the length of the focal chord______

  • A 25
  • B 35
  • C 45
  • D 55

Question - 4

A focal chord of the parabola y2 = 16x is tangent to the circle (x - 6)2 + y2 = 2 then fnd sum of possible values of slope of this chord______

  • A 1
  • B 2
  • C 3
  • D 4

Question - 5

The line x - 1= 0 is the directrix of the parabola y2 - kx + 8 = 0. Then frnd the product of values of k________

  • A 32
  • B -32
  • C 22
  • D -22

Question - 6

The equation of latus rectum of a parabola is x + y = 8 and the equation of the tangent at the vertex is x + y = 12, if the length ofthe latus rectum is \(k\sqrt2\) then find k_______

  • A 4
  • B 8
  • C 12
  • D 24

Question - 7

Find the latus rectum ofthe parabola y2 = 4ax whose focal is PSQ such that SP = 3 & SQ = 2.______

  • A 2.8080
  • B 3.80
  • C 4.80
  • D 6.80

Question - 8

An equilateral triangle is inscribed in the paraboia y2 = 4ax, whose vertex is at the vertex of the parabola. Ifthe length of its side is ka\(\sqrt3\) then frnd k._____

  • A 2
  • B 6
  • C 8
  • D 12

Question - 9

If the distance between directrix and latus rectum ofa parabola is 4 units, then find the length of its latus rectum____

  • A 4
  • B 12
  • C 8
  • D 16

Question - 10

Find the length of latus rectum of the parabola 5y2 - 3x - 8y - 1= 0_______

  • A 0.20
  • B 0.40
  • C 0.60
  • D 0.80
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