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

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

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

Salim Ahmed Kawsar

Correct Answer - `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`

5 views Answered 2023-02-05 15:29

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