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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.
$straight x squared space equals negative 9 straight y$

straight x squared space equals negative 9 straight y space or space straight x squared plus 9 straight y equals 0

It is equation of parabola in the standard form

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

and it open towards.
Comparing the equation with

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we have

negative 4 straight a space equals negative 9 space or space straight a equals 9 over 4

∴ (i) the focus is S(0, -a)

left right arrow

open parentheses 0 comma space fraction numerator negative 9 over denominator 4 end fraction close parentheses

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

straight y minus 9 over 4 space equals space 0 space or space 4 straight y minus 9 space equals 0

(v) the length of the latus rectum = 4a =

4 cross times 9 over 4 equals 9

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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.

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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)

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