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To find the p-value for a parabola given its focus and directrix, first identify the coordinates of the focus (F) and the equation of the directrix (a line). The p-value represents the distance from the vertex of the parabola to the focus (or the vertex to the directrix), which is half the distance between them. Calculate this distance using the formula for distance between a point and a line, or by measuring the distance from the vertex to either the focus or the directrix. The p-value is then the absolute value of this distance.
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What is the equation of the parabola with focuse (07) and the directrix y1?
To find the equation of the parabola with focus at (0, 7) and directrix ( y = 1 ), we first determine the vertex, which is the midpoint between the focus and the directrix. The vertex is at ( (0, 4) ). The distance from the vertex to the focus is 3, so the parabola opens upward. The equation of the parabola can be expressed as ( (x - h)^2 = 4p(y - k) ), where ( (h, k) ) is the vertex and ( p ) is the distance from the vertex to the focus. Thus, the equation is ( x^2 = 12(y - 4) ).
How would you find the vertex p value focus directrix and focal width of negative one fourth x squared equals y?
-(1/4) x2 = y . . . putting this in the standard form x2 = 4cy it becomes : x2 = 4*(-1)y = -4y. This tells us that the parabola is a downward opening parabola with its vertex at the origin(0.0). The focus is at a distance of -1 from the vertex, that is (0,-1). The directrix is equidistant to the focus but on the opposite side of the vertex and is thus the line y = 1. The length of the chord passing through the focus and perpendicular to the major axis is called the Latus Rectum and has a length of 4c. As c = -1 then the length is 4 but again shows as a negative value as it is "below" the vertex.
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How would you find the vertex p value focus directrix and focal width of negative one fourth x squared equals y?
-(1/4) x2 = y . . . putting this in the standard form x2 = 4cy it becomes : x2 = 4*(-1)y = -4y. This tells us that the parabola is a downward opening parabola with its vertex at the origin(0.0). The focus is at a distance of -1 from the vertex, that is (0,-1). The directrix is equidistant to the focus but on the opposite side of the vertex and is thus the line y = 1. The length of the chord passing through the focus and perpendicular to the major axis is called the Latus Rectum and has a length of 4c. As c = -1 then the length is 4 but again shows as a negative value as it is "below" the vertex.
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