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Conic Section

Long Answer Type

71. An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2m from the vertex of the parabola?

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Short Answer Type

72. Find the equation of the parabola having focus at point (2, 0) and the straight line x + 2 = 0 as the directrix.

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73. Find the equation of the parabola with focus at point S(2, –1) and x y + – 4 = 0 as the directrix.

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74. Find the equation of the parabola having focus at point (0, –2) and the straight line y = 1 as the directrix.

Solution not provided.
Ans. $straight x squared plus 6 straight y plus 3 equals 0$

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75.

If a parabolic reflector is $8 square root of 30 space cm$ in diameter and 20 cm deep, find the distance of its focus S from the vertex.

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76. The focus of a parabolic mirror is at a distance of 6 cm from the vertex. If the mirror is 20 cm deep, find the vertical diameter of the mirror.

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Long Answer Type

77. An arch is in the form of parabola with its axis vertical. The arch is 8 m high and 4 m wide at the base level. How wide is the arch at a height of 2 m above the vertex?

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Short Answer Type

78. Find the area of the triangle formed by joining the vertex of parabola y² = 8x and the two ends of the latus rectum.

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79. Find the area of the triangle formed by joining the vertex of the parabola x² = 64y to the two ends of its latus rectum.

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80.

An equilateral triangle is inscribed in a parabola y² = 16x, where one vertex is at the vertex of the parabola. Find
(i) Length of each side of the triangle (ii) the area of the triangle

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