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Conic Section

Short Answer Type

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

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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

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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

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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

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

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

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

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

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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.

The vertex of the parabola is O (0, 0) and the axis is along x-axis (y = 0).
$rightwards double arrow$ The equation of the parabola is $straight y squared equals 4 ax$ ...(i)
Since it passes through the point (2, 3)
∴ $3 squared space equals space 4 straight a left parenthesis 2 right parenthesis space rightwards double arrow space 9 space equals space 8 straight a space space space space rightwards double arrow space space straight a equals 9 over 8$
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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)