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What is the equation of the directrix of the parabola?
The answer depends on the form in which the equation of the parabola is given. For y^2 = 4ax the directrix is x = -2a.
What is the focus and directrix of y equals 8x squared?
Need set of point parabola passes through.X = 1Y = 8----------------(1, 8)For focus,X2 = 4pYinsert values, solve for p(1)2 = 4p(8)= 1/32=======focus- 1/32=======directrix( long time since I have done this. Formula is correct, check my math )
What is the standard form of the equation of the parabola with vertex 00 and directrix y4?
Assuming the vertex is 0,0 and the directrix is y=4 x^2=0
How the equation of directrix is y plus a equals 0 in parabola?
Restate the question: "In the parabola y = ax2, why is the equation of the directrix y+a = 0?If this is not your question, please clarify and ask the question again.The "locus" definition of a parabola says that a parabola is the set of all points which are the same distance from a given point and a given line. The point is called the focus, F. The line is called the directrix, d.With a little foresight, we set things up so that the vertex of the parabola is at the origin O, and the parabola opens upward: Let the equation of d be y = -a ... which can be written y+a+0 ... , and let F be (0,a). If you make a sketch, it is clear that the distance from O to F is a, and the shortest (perpendicular) distance from O to d is also a. This shows that the origin is on the parabola.To set up an equation, we need formulas for the distance from a point P(x,y) on the parabola to F and to d:Mark a point in the first quadrant and label it P(x,y). The distance from P to the x-axis is y, and the distance from the x-axis to d is a. The distance from P to d is y+a.To find the distance from P to F, we use the distance formula:PF = sqrt((x2-x1)2+(y2-y1)2) = sqrt((x-0)2+(y-a)2) = sqrt(x2+(y-a)2).If P is on the parabola then PF = Pd sqrt(x2+(y-a)2) = y+a.Square both sides to get x2+(y-a)2 = (y+a)2 x2+y2-2ay+a2 = y2+2ay+a2 x2-2ay = 2ay x2 = 4ay 4ay = x2 y = (1/(4a))x2.So, y+a=0 isn't the directrix of y=ax2 after all, it's actually the directix of y=(1/(4a))x2.Common practice is to replace a by p and switch the equation around:y=(1/(4p))x2 4py=x2 x2=4py. This is the equation of a parabola with focus (0,p) and directrix y=-p.
What does 4 stands for in equation of parabola square of square of y equals 4ax?
A parabola with an equation, y2 = 4ax has its vertex at the origin and opens to the right. It's not just the '4' that is important, it's '4a' that matters. This type of parabola has a directrix at x = -a, and a focus at (a, 0). By writing the equation as it is, the position of the directrix and focus are readily identifiable. For example, y2 = 2.4x doesn't say a great deal. Re-writing the equation of the parabola as y2 = 4*(0.6)x tells us immediately that the directrix is at x = -0.6 and the focus is at (0.6, 0)
What is the equation of the quadratic graph with a focus of (3 6) and a directrix of y 4?
For a parabola with a y=... directrix, it is of the form: (x - h)^2 = 4p(y - k) with vertex (h, k), focus (h, k + p) and directrix y = k - p With a focus of (3, 6) and a directrix of y = 4, this means: (h, k + p) = (3, 6) → k + p = 6 y = k - p = 4 → k = 5, p = 1 (solving the simultaneous equations) → vertex is (3, 5) → parabola is (x - 3)^2 = 4(y - 5) which can be rearranged into y = 1/4 x^2 - 3/2 x + 29/4
Using the given equations of parabolas find the focus the directrix and the equation of the axis of symmetry of x2 -8y?
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What is the relationship between the focus and directrix?
i assume this is locus you are talking about, in which case: they are both the same distance from the vertex - focal length, focus is a point: P(x,y) and directrix is a horizontal line e.g. y=-1
What is the equation of the directrix of the parabola?
The answer depends on the form in which the equation of the parabola is given. For y^2 = 4ax the directrix is x = -2a.
What is the focus and directrix of y equals 8x squared?
Need set of point parabola passes through.X = 1Y = 8----------------(1, 8)For focus,X2 = 4pYinsert values, solve for p(1)2 = 4p(8)= 1/32=======focus- 1/32=======directrix( long time since I have done this. Formula is correct, check my math )
What is the standard form of the equation of the parabola with vertex 00 and directrix y4?
Assuming the vertex is 0,0 and the directrix is y=4 x^2=0
What is the axis of symmetry for the parabola with vertex (-2 -4) and directrix y 1?
The axis of symmetry is x = -2.
What is the focus of a parabola?
The focus of a parabola is a fixed point that lies on the axis of the parabola "p" units from the vertex. It can be found by the parabola equations in standard form: (x-h)^2=4p(y-k) or (y-k)^2=4p(x-h) depending on the shape of the parabola. The vertex is defined by (h,k). Solve for p and count that many units from the vertex in the direction away from the directrix. (your focus should be inside the curve of your parabola)
How the equation of directrix is y plus a equals 0 in parabola?
Restate the question: "In the parabola y = ax2, why is the equation of the directrix y+a = 0?If this is not your question, please clarify and ask the question again.The "locus" definition of a parabola says that a parabola is the set of all points which are the same distance from a given point and a given line. The point is called the focus, F. The line is called the directrix, d.With a little foresight, we set things up so that the vertex of the parabola is at the origin O, and the parabola opens upward: Let the equation of d be y = -a ... which can be written y+a+0 ... , and let F be (0,a). If you make a sketch, it is clear that the distance from O to F is a, and the shortest (perpendicular) distance from O to d is also a. This shows that the origin is on the parabola.To set up an equation, we need formulas for the distance from a point P(x,y) on the parabola to F and to d:Mark a point in the first quadrant and label it P(x,y). The distance from P to the x-axis is y, and the distance from the x-axis to d is a. The distance from P to d is y+a.To find the distance from P to F, we use the distance formula:PF = sqrt((x2-x1)2+(y2-y1)2) = sqrt((x-0)2+(y-a)2) = sqrt(x2+(y-a)2).If P is on the parabola then PF = Pd sqrt(x2+(y-a)2) = y+a.Square both sides to get x2+(y-a)2 = (y+a)2 x2+y2-2ay+a2 = y2+2ay+a2 x2-2ay = 2ay x2 = 4ay 4ay = x2 y = (1/(4a))x2.So, y+a=0 isn't the directrix of y=ax2 after all, it's actually the directix of y=(1/(4a))x2.Common practice is to replace a by p and switch the equation around:y=(1/(4p))x2 4py=x2 x2=4py. This is the equation of a parabola with focus (0,p) and directrix y=-p.
What does 4 stands for in equation of parabola square of square of y equals 4ax?
A parabola with an equation, y2 = 4ax has its vertex at the origin and opens to the right. It's not just the '4' that is important, it's '4a' that matters. This type of parabola has a directrix at x = -a, and a focus at (a, 0). By writing the equation as it is, the position of the directrix and focus are readily identifiable. For example, y2 = 2.4x doesn't say a great deal. Re-writing the equation of the parabola as y2 = 4*(0.6)x tells us immediately that the directrix is at x = -0.6 and the focus is at (0.6, 0)
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.
A parabola is a set of all points that?
are the same distance from a point (known as its focus) and a line (known as its directrix)are given by y=x2, where x is realThere are other characterisations.Apex Answer: are the same distance from a point and a line.
