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Mathematics : Conic Section

Short Answer Type

131.

Find the equation for the ellipse that satisfies the given condition:
Ends of major axis $space space left parenthesis 0 comma space plus-or-minus square root of 5 right parenthesis comma space$ ends of minor axis $left parenthesis plus-or-minus 1 comma space 0 right parenthesis$

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132.

Find the equation for the ellipse that satisfies the given condition:
Ends of major axis 18, foci $left parenthesis plus-or-minus 3 comma space 0 right parenthesis$

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133.

Find the equation for the ellipse that satisfies the given condition:
Length of minor axis 8, foci $left parenthesis 0 comma space plus-or-minus 3 right parenthesis$

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134.

Find the equation for the ellipse that satisfies the given condition:
Foci, $left parenthesis 0 comma space plus-or-minus 3 right parenthesis comma space straight a space equals space 5$

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135.

Find the equation for the ellipse that satisfies the given condition:
Foci $space space left parenthesis plus-or-minus 5 comma space 0 right parenthesis comma space space straight a equals 8$

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136.

Find the equation for the ellipse that satisfies the given condition:
b = 5, c = 3, axis along the y-axis.

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137.

Find the equation for the ellipse that satisfies the given condition:
Centre (0, 0), major axis on y-axis and passing through points A (3, 2), B (1, 6).

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138.

Find the equation for the ellipse that satisfies the given condition:
Major axis on x-axis, passing through points A (4, 3) and B (6, 2).

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139. A rod of length 12cm moves with its ends always touching the co-ordinates axes. Determine the equation of the locus of a point P on the rod which is 3 cm from the end in contact with the x-axis .

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140.

Find the eccentricity of an ellipse if its latus rectum is $1 half$ of its minor axis.

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