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If the focus and vertex of a parabola ar...

If the focus and vertex of a parabola are the points (0, 2) and (0, 4), respectively, then find the equation

Text Solution

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The correct Answer is:
`x^(2)+8y=32`
Focus is (0,2) and vertex is (0,4).
so, axis of the parabola is y-axis.
Also, parabola is concave downward.
Distance between focus and directrix is a=2.
`:.` Latus rectum = 4a=8
So, using equation `(x-h)^(2)=4a(y-k)`, equation of parabola is `(x-0)^(2)=-8(y-4)`
`or" "x^(2)+8y=32`
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Knowledge Check

  • If the coordinates of vertex and focus of a parabola be (2,1) & (2,3) respectively, then the axis of the parabola will be

    A
    a) Y-axis
    B
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    C
    c)Parallel to the Y-axis
    D
    d)Parallel to the X-axis

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