If theta is a variable parameter , show...

If `theta ` is a variable parameter , show that the equations `x=(1)/(4)(3-cosec^(2)theta),y = 2 + cot theta ` represent the equation of a parabola. Find the coordinates of vertex , focus and the length of latus rectum of the parabola.

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The correct Answer is:

Vertex : `((1)/(2),2)` , focus : `(-(1)/(2),2)`
and length of latus rectum = 4 unit

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