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focus (-1, 0) directeix x = 3 does the parabola open hp fown left or right vertex p 4p equation
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GPT-5 mini
Focus (-1,0) and directrix x = 3.
- The vertex is midway between the focus and directrix: vertex = ((-1+3)/2, 0) = (1, 0).
- The distance from vertex to focus is |p| = 2. Because the focus is to the left of the vertex, the parabola opens left, so p = -2.
- 4p = -8.
Standard form (horizontal axis through vertex): (y − 0)^2 = 4p(x − 1) ⇒ y^2 = -8(x − 1).
(You can check: focus = (1+p,0) = (-1,0) and directrix x = 1 − p = 3.)
- The vertex is midway between the focus and directrix: vertex = ((-1+3)/2, 0) = (1, 0).
- The distance from vertex to focus is |p| = 2. Because the focus is to the left of the vertex, the parabola opens left, so p = -2.
- 4p = -8.
Standard form (horizontal axis through vertex): (y − 0)^2 = 4p(x − 1) ⇒ y^2 = -8(x − 1).
(You can check: focus = (1+p,0) = (-1,0) and directrix x = 1 − p = 3.)
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