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51. In the following, find the co-ordinates of the focus, axis of the parabola, the equation of the directrix and length of the latus rectum.
$space space space space straight x squared equals 6 straight y$

space space space space straight x squared equals 6 straight y

It is the equation of a parabola in the standard form

straight x squared equals 4 ay comma space straight a greater than 0

and open upwards.
Comparing it with

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∴ (i) co-ordinates of the focus are S(0, a)

left right arrow

open parentheses 0 comma space 3 over 2 close parentheses

(ii) equation of axis of parabola is x = 0 (y-axis)
(iii) equation of tangent at the origin is y = 0 (x-axis)
(iv) equation of directrix is y + a = 0 or

straight y plus 3 over 2 equals 0 space or space 2 straight y plus 3 equals 0

(v) length of the latus rectum =

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79 Views

52. In the following, find the co-ordinates of the focus, axis of the parabola, the equation of the directrix and length of the latus rectum.

straight x squared space equals negative 9 straight y

100 Views

53. Find: the co-ordinates of the focus and the vertex, the equations of axis, tangent at the vertex and directrix, the length of latus rectum of the parabola.

2 straight y squared minus 9 straight x equals 0

98 Views

54. Find: the co-ordinates of the focus and the vertex, the equations of axis, tangent at the vertex and directrix, the length of latus rectum of the parabola.

4 straight x squared plus 9 straight y equals 0

87 Views

55. Find the equation of the parabola whose focus is at point S (2, 5) and the directrix is line 3x + 4y + 1 = 0.

429 Views

56. Find the equation of the parabola whose vertex is at (0, 0) and the focus is at point S (5, 0).

104 Views

57. Find the equation of the parabola whose vertex is at (0, 0) and the focus is at point (-3, 0).

83 Views

58. Find the equation of the parabola whose vertex is at (0, 0) and focus is at (0, – 2).

92 Views

59. Find the equation of the parabola that satisfying the following condition:
Vertex (0,0) passing through (2,3) and axis is along x-axis.

80 Views

60. Find the equation of the parabola that satisfying the following condition:
Vertex at (0,0), symmetrical about y-axis and passing through the point (2, –3)

87 Views