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Conic Section

Short Answer Type

91. Find equation of parabola for vertex at origin, focus (0, –2), directrix y = 2.

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92. Find equation of parabola for vertex at origin, focus (–3, 0), directrix x = 3.

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93. Find equation of parabola for vertex at origin, axis along the y-axis and passing through the point (3, 2).

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94. Find equation of parabola for vertex at the origin, symmetric with respect to the x-axis and passing through point (2, –3).

Solution not provided.
Ans. $2 straight y squared equals 9 straight x$

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Long Answer Type

95.

The cable of a uniformly loaded suspension bridge hang in the form of a parabola.
The roadway which is horizontal and 100 m long, is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to a roadway 18 m from the middle.

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96. Verify that the locus of a point P which moves so that the sum of its distance from points S₁ (– 4,0) and S₂ (4,0) is 10, is an ellipse.

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97. In the following, find the co-ordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.

straight x squared over 36 plus straight y squared over 16 equals 1

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98. In the following, find the co-ordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.

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99. In the following equation, Find the co-ordinates of foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of latus rectum of the ellipse.

16 straight x squared plus straight y squared equals 16

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100. In the following equation, Find the co-ordinates of foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of latus rectum of the ellipse.

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