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Find the co-operate of the focus, the eq...

Find the co-operate of the focus, the equation of the directrix and latus rectum of the parabola `y^(2) = 20x`.

Text Solution

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The given equation involves `y^(2)`, so the axis of symmetry is x-axis.
The coefficient of x is positive , so the parabola opens the right. Comparing with the given equation `y^(2) = 4ax`, we get 4a = 20
`rArr a = 5`
Thus, the focus of the parabola is (5, 0) and the equation of the directrix of the parabola is `x = -5`
Length of the latus rectum is `4a = 4 xx 5 = 20`
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