38. If the differential equation^

represents a family of hyperbolas, then
the eccentricity is:

(a) √^ (b) √^ (c) √^ (d) √^

39. The equation of the hyperbolas
    whose eccentricity is 5/4 and distance
    between foci is 10, is given by:

(a)^
(b)
= 1 (c)

(d)^

40. The eccentricity of the hyperbola
    25 = 144 is:

(a) √ (b) √ (c) √ (d) √^

41. If e and e’ are the eccentricities of a
    hyperbola and its conjugate respectively,

then is equal to:

(a) 0 (b) 1 (c) 2 (d)^

42. What is the difference of the focal
    distances of any point on the hyperbola?
    (a) Eccentricity (b) Distance between
    foci
    (c) Length of transverse axis (d) Length
    of semi transverse axis


43. The foci of the ellipse^
    = 1
    where μ < 4 and the foci of the hyperbola

=

coincide. What is the value of

(a) 1 (b) 5 (c) 7 (d) 9

44. What is the area of the triangle
    formed by the lines joining the vertex of

the parabola = 12y to the end of the

latusrectum?

(a) 9 sq units (b) 12 sq units (c) 14 sq

units

(d) 18 sq units

45. What is the focal distance at any
    point P( ) on the parabola = 4ax?
    (a) (b) (c) a (d) a +


46. What are the points of intersection of
    the curve 4 = 1 with its conjugate
    axis?
    (a) (1/2, 0) and (-1/2, 0)
    (b) (0, 2) and (0, -2)
    (c) (0, 3) and (0, -3)
    (d) No such point exists


47. 
    

    Find the equation of circle which is
    drawn taking the focus of ellipse^

    
    

    1 as the end points of its diameter.

    
    

(a) = (b) =

(c) = ( ) (d)

= ( )

48. What are the equation of the
    directrices of the ellipse 25
    ?
    (a) 3x ± 25= 0 (b) 3y ± 25= 0 (c) x ± 15=
    0 (d) y ± 25= 0


49. Let E be the ellipse^
    = 1 and C
    be the circle. Let P= (1, 2)
    and Q= (2, 1). Which one of the following
    is correct?
    (a) Q lies inside C but outside E (b) Q lies
    outside both C and E (c) P lies inside
    both C and E (d) P lies inside C but
    outside E