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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.
$2 straight y squared minus 9 straight x equals 0$

2 straight y squared minus 9 straight x equals 0 space rightwards double arrow space straight y squared equals 9 over 2 straight x

It is equation of a parabola in the standard form

straight y squared equals 4 ax comma space straight a greater than 0

and open to the right.
Comparing it with

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we have

space space 4 straight a equals 9 over 2 space rightwards double arrow space straight a space equals space 9 over 8

∴ Co-ordinate of focus are S (a, 0)

left right arrow

open parentheses 9 over 8 comma space 0 close parentheses

Co-ordinates of vertex are (0, 0)

Equation of axis of parabola is y = 0 (x-axis).
Equation of tangent at the origin is x = 0 (y-axis).
Equation of directrix is x + a = 0 or

space space space straight x plus 9 over 8 equals 0 space or space 8 straight x plus 9 equals 0

Latus rectum = 4a =

4 cross times 9 over 8 equals 9 over 2

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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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