What is Directrix mean in math?

A parabola is set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola, and the line is called the directrix . The directrix is perpendicular to the axis of symmetry of a parabola and does not touch the parabola.

What is the Directrix in simple terms?

Definition of directrix

1 archaic : directress. 2 : a fixed curve with which a generatrix maintains a given relationship in generating a geometric figure specifically : a straight line the distance to which from any point of a conic section is in fixed ratio to the distance from the same point to a focus.

How do you find the Directrix?

The directrix of a parabola can be found, by knowing the axis of the parabola, and the vertex of the parabola. For an equation of the parabola in standard form y² = 4ax, with focus at (a, 0), axis as the x-axis, the equation of the directrix of this parabola is x + a = 0 .

What is Directrix equation?

Equation of directrix is y = -a. i.e. y = -½ is the equation of directrix. Vertex of the parabola is (0,0).

How do you find the Directrix of a parabola given an equation?

We use the equation y=k−p y = k − p to find the directrix. Therefore, The focus of the is parabola (4,−3) and the directrix is y=1 .

Focus and directrix introduction | Conic sections | Algebra II | Khan Academy

What is a Directrix of a hyperbola?

Directrix of a hyperbola is a straight line that is used in generating a curve. It can also be defined as the line from which the hyperbola curves away from. This line is perpendicular to the axis of symmetry. The equation of directrix is: x = ± a 2 a 2 + b 2.

What is the Directrix used for?

Key Terms. directrix: A line used to define a curve or surface, especially a line from which any point on a parabola curve has a distance equal to the distance from the focus.

What is Directrix in conic section?

In the conic section, a directrix is a line that is together with the point called the focus. It helps to define the conic section as the locus of points, such that the distance from the focus is proportional to the horizontal distance from the line, called the directrix, and “r” being the constant of proportionality.

What object is defined using a Directrix and a focus?

A parabola is the set of all points equidistant from a point (called the "focus") and a line (called the "directrix").

What is the Directrix of a circle?

In a right circular cylinder, the directrix is a circle. The axis of this cylinder is a line through the centre of the circle, the line being perpendicular to the plane of the circle.

What is 1 4p in a parabola?

Equation of a Parabola in Terms of the Coordinates of the Focus. Another way of expressing the equation of a parabola is in terms of the coordinates of the vertex (h,k) and the focus. Using Pythagoras's Theorem we can prove that the coefficient ɑ = 1/4p, where p is the distance from the focus to the vertex.

What is a Directrix of a parabola?

A parabola is set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola, and the line is called the directrix . The directrix is perpendicular to the axis of symmetry of a parabola and does not touch the parabola.

When the parabola opens to the left the Directrix is?

The directrix is the line x = h - p. The axis is the line y = k. If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left.

How do you find the Directrix of an ellipse?

For the ellipse x2a2+y2b2=1 x 2 a 2 + y 2 b 2 = 1 , the equations of the two directrix of ellipse is x = +a/e, and x = -a/e. The directrix of the ellipse is equidistant from the center of the ellipse. The two directrices of the ellipse are parallel to each other and are also parallel to the minor axis of ellipse.

What is Directrix of ellipse?

What is directrix and eccentricity of ellipse? In ellipse, the fixed line parallel to minor axis, at a distance of d from the center is called directrix of ellipse. Eccentricity (e) is measured as the elongation of ellipse. The value of 'e' lies between 0 and 1, for ellipse.

What is the equation of the directrix of the parabola y 3?

Explanation: The axis of the parabola is perpendicular to the directrix through the focus S. So, its equation is x = − 3, in the negative direction of y-axis.. The vertex V is on the axis, midway in-between focus S and directrix.

How do you solve a parabola equation?

What is the parabola formula?

The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax. Some of the important terms below are helpful to understand the features and parts of a parabola. Focus: The point (a, 0) is the focus of the parabola.