Conic section test 1

Question no. 1

If any point on a hyperbola is (3tanθ , 2secθ) , then what is the eccentricity of the hyperbola ?
  3/2
  5/2
  √11 / 2
  √13/2

Question no. 2

The curve y²= -4ax (a>0) lies in
  first and fourth quadrants
  first and second quadrants
  second and third quadrants
  third and fourth quadrants

Question no. 3

What is the maximum number of the parabolas that can be drawn through these points as end points of latusrectum ?
  only one
  two
  four
  infinite

Question no. 4

The sum of the focal distance of a point on an ellipse is constant and equal to
  length of minor axis
  length of major axis
  length of latus rectum
  sum of the lengths of semi major and semi minor axis.

Question no. 5

Two parabolas y² = 4ax and x² = 4ay intersect
  at two points on the line y =x
  only at the origin
  at the three points one of which lies on y+x = 0
  only at (4a ,4a)

Question no. 6

The equation 2x² - 3y² - 6 = 0 represents
  a circle
  a parabola
  an ellipse
  a hyperbola

Question no. 7

Let E be the ellipse x²/9 + y²/4 = 1 and C be the circle x² + y² =9 . Let P (1,2) and Q (2,1) . Which one of the following is correct?
  Q lies inside C but outside E
  Q lies outside both C and E
  P lies inside both C and E
  P lies inside C but outside E

Question no. 8

The centre of the circle (x-2a)(x-2b) + (y-2c)(y-2d) = 0 is
  (2a , 2c)
  (2b ,2d)
  (a+b , c+d)
  (a-b , c-d)

Question no. 9

Let P(x,y) be any point on the ellipse 25x² + 16y² = 400 . If Q(0,3) and R(0, -3) are two points , then what is (PQ + PR) equal to ?
  12
  10
  8
  6

Question no. 10

The focus of the parabola x²=-16y is
  (4,0)
  (0,4)
  (-4 ,0)
  (0,-4)

Question no. 11

The ends of latus rectum of parabola x² + 8y =0
  (-4 ,-2) and (4,2)
  (4 ,-2) and (-4,2)
  (-4 ,-2) and (4,-2)
  (-4 ,2) and (4,2)

Question no. 12

Foci and directrices of the parabola x² = -8ay are
  (0,-2a ) and y=2a
  (0,-2a ) and y=-2a
  (2a,0 ) and x=-2a
  (-2a ,0 ) and x=2a

Question no. 13

The equation of the ellipse whose vertices are (∓5,0) and foci at (∓4, 0) is
  x²/25 + y²/9 =1
  x²/9 + y²/25 =1
  x²/16 + y²/25 =1
  x²/25 + y²/16 =1

Question no. 14

The difference of focal distances of any point on hyperbola is equal to
  latus rectum
  semi-transverse axis
  transverse axis
  semi-latus rectum

Question no. 15

What is the locus of points , the difference of whose distances from two points being constant?
  hyperbola
  ellipse
  parabola
  pair of straight lines