## What is the focus and directrix of a parabola?

They can also be viewed as the set of all points whose distance from a certain point (the focus) is equal to their distance from a certain line (the directrix ). Want to learn more about focus and directrix of a parabola? Check out this video. Given the focus and the directrix of a parabola, we can find the parabola’s equation.

What is the focus of a parabola in jsxgraph?

You can explore the concept of directrix and focus of a parabola in the following JSXGraph (it’s not a fixed image). Quick background: The parabola below has focus at F, and point P is at any position on the parabola. Point Q is the foot of the perpendicular to the directrix through P.

Where can I find an interactive parabola graph?

Interactive parabola graphs You can explore various parabolas on this page, and see the effect of changing parameters (by dragging various points around). For background information on what’s going on, and more explanation, see: You can explore the concept of directrix and focus of a parabola in the following JSXGraph (it’s not a fixed image).

### Where does the equation of a parabola come from?

The equation of a parabola is derived from the focus and directrix, and then the general formula is used to solve an example. This is the currently selected item. Posted 6 years ago.

What are the equations for focus and directrix?

In the equations y=a (x-h)^2+k and x=a (y-k)^2+h where a=1/4p , (h,k ) represents vertex and p is the distance between focus and vertex . In the above equations (a,b) represents FOCUS not VERTEX . In the first one directrix is y=k and in second one directrix is x=k .

How to find the equation of a parabola?

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 4). Since the vertex is at (0, 0) and the focus is at (0, 5) which lies on y-axis, the y-axis is the axis of the parabola. Hence, the equation of the parabola is x2= 4ay.

#### Which is the Y axis of a parabola?

Since the vertex is at (0, 0) and the focus is at (0, 5) which lies on y-axis, the y-axis is the axis of the parabola. Hence, the equation of the parabola is x2= 4ay.

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 .

What is the Directrix of 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.

Are circles parabolas?

No, a circle is not the same as a parabola. A parabola is formed by the intersection of a cone and a plane parallel to the axis of the cone. A circle is formed when the intersecting plane is perpendicular to the axis of the cone.

## How do you find the directrix of a circle?

The directrix formula is x = -p Since p = 2, then x = – (2) = -2 The directrix is x = -2.

What is the purpose of the focus and directrix?

What are the focus and directrix of a parabola? Parabolas are commonly known as the graphs of quadratic functions. They can also be viewed as the set of all points whose distance from a certain point (the focus) is equal to their distance from a certain line (the directrix).

What is the difference between a vertex a focus and a directrix?

The focus is “p” units from the vertex. Since the focus is “inside” the parabola and since this is a “right side up” graph, the focus has to be above the vertex. Then the focus is one unit above the vertex, at (0, 1), and the directrix is the horizontal line y = –1, one unit below the vertex.

### Do circles directrix?

A circle is a limiting case and is not defined by a focus and directrix in the Euclidean plane. The eccentricity of a circle is defined to be zero and its focus is the center of the circle, but its directrix can only be taken as the line at infinity in the projective plane.

Does a circle have a focus and directrix?

A circle is determined by one focus. A circle is the set of all points in a plane at a given distance from the focus (center). A parabola is determined by a focus and a directrix (a line). A parabola is the set of points in a plane such that the distance from the focus equals the distance to the directrix.

What is the difference between circle and parabola?

is that circle is (geometry) a two-dimensional geometric figure, a line, consisting of the set of all those points in a plane that are equally distant from another point while parabola is (geometry) the conic section formed by the intersection of a cone with a plane parallel to a tangent plane to the cone; the locus of …