0
Still curious? Ask our experts.
Chat with our AI personalities
Lao
Maxine
BlakeAdd your answer:
Earn +20 pts
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)
