The vertex of a parabola is (2, 2) and the coordinats of its two extremities of latus rectum are `(-2,0)` and (6, 0). Then find the equation of the pa

Question

The vertex of a parabola is (2, 2) and the coordinats of its two extremities of latus rectum are `(-2,0)` and (6, 0). Then find the equation of the pa

The vertex of a parabola is (2, 2) and the coordinats of its two extremities of latus rectum are `(-2,0)` and (6, 0). Then find the equation of the parabola.

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - `(x-2)^(2)=-8(y-2)`
Focus is midpoint of the extremities of latus rectum.
Thus, focus is (2,0).
Distance between focus and vertex is a=2.
Also, axis of the parabola is x=2 and parabola is concave downward as focus lies below the vertex.
Therefore, using equation `(x-h)^(2)=-4a(y-k)`, required equation of parabola is
`(x-2)^(2)=-8(y-2)`