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What is the equation of a parabola with vertex (0 0) and directrix x -3.?
The equation of a parabola with vertex at (0, 0) and a directrix of ( x = -3 ) opens to the right, as the directrix is a vertical line. The distance from the vertex to the directrix is 3 units. The standard form of the equation for a horizontally-opening parabola is given by ( y^2 = 4px ), where ( p ) is the distance from the vertex to the directrix. Therefore, with ( p = 3 ), the equation is ( y^2 = 12x ).
How do you get directrix of a parabola?
The directrix of a parabola can be found using its standard form equation. For a parabola that opens upwards or downwards, given by (y = ax^2 + bx + c), the directrix is located at (y = k - \frac{1}{4p}), where (k) is the vertex's y-coordinate and (p) is the distance from the vertex to the focus. For a parabola that opens sideways, the directrix is given by (x = h - \frac{1}{4p}), where (h) is the vertex's x-coordinate. The value of (p) can be determined based on the coefficients of the quadratic equation.
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 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)
Is it true or false that the directrix and focus are different distances from a given point on a parabola?
True. In a parabola, any point on the curve is equidistant from the focus and the directrix. This means that while the distances to the focus and directrix are equal for points on the parabola, they are different distances from any point not on the parabola.
What is the equation of a parabola with vertex (0 0) and directrix x -3.?
The equation of a parabola with vertex at (0, 0) and a directrix of ( x = -3 ) opens to the right, as the directrix is a vertical line. The distance from the vertex to the directrix is 3 units. The standard form of the equation for a horizontally-opening parabola is given by ( y^2 = 4px ), where ( p ) is the distance from the vertex to the directrix. Therefore, with ( p = 3 ), the equation is ( y^2 = 12x ).
What is the line that divides a parabola?
It is the axis. NOT the directrix which does not even touch the parabola.
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 standard equation of a parabola that opens up or down and whose vertex is at the origin?
focus , directrix
How do you get directrix of a parabola?
The directrix of a parabola can be found using its standard form equation. For a parabola that opens upwards or downwards, given by (y = ax^2 + bx + c), the directrix is located at (y = k - \frac{1}{4p}), where (k) is the vertex's y-coordinate and (p) is the distance from the vertex to the focus. For a parabola that opens sideways, the directrix is given by (x = h - \frac{1}{4p}), where (h) is the vertex's x-coordinate. The value of (p) can be determined based on the coefficients of the quadratic equation.
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)
The is the extreme point of a parabola and is located halfway between the focus and directrix?
The vertex -- the closest point on the parabola to the directrix.
What is the midpoint of the parabola between the focus and the directrix?
It is the apex of the parabola.
What is the directrix of a parabola?
"From the geometric point of view, the given point is the focus of the parabola and the given line is its directrix. It can be shown that the line of symmetry of the parabola is the line perpendicular to the directrix through the focus. The vertex of the parabola is the point of the parabola that is closest to both the focus and directrix."-http://www.personal.kent.edu/~rmuhamma/Algorithms/MyAlgorithms/parabola.htm"A line perpendicular to the axis of symmetry used in the definition of a parabola. A parabola is defined as follows: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus, or set of points, such that the distance to the focus equals the distance to the directrix."-http://www.mathwords.com/d/directrix_parabola.htm
If the distance from the green point on the parabola to the parabola's focus is 7 What is the distance from the green point to the directrix?
In a parabola, the distance from any point on the curve to the focus is equal to the distance from that point to the directrix. If the distance from the green point on the parabola to the focus is 7, then the distance from the green point to the directrix is also 7. Therefore, the distance from the green point to the directrix is 7.
A line that helps define a parabola?
directrix
What geometric shape has focus and directrix?
A parabola.
