What is the focus and directrix of a circle?

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 directrix of a conic?

The directrix of a conic section is the line which, together with the point known as the focus, serves to define a conic section as the locus of points whose distance from the focus is proportional to the horizontal distance from the directrix, with being the constant of proportionality.

Is circle A conic?

The circle is the simplest and best known conic section. As a conic section, the circle is the intersection of a plane perpendicular to the cone’s axis.

What conic section has no directrix?

Ellipse (e = 1/2), parabola (e = 1) and hyperbola (e = 2) with fixed focus F and directrix L (e = ∞). The red circle (e = 0) is included for reference; it does not have a directrix in the plane.

What is directrix of a circle?

Go by definition. A directrix of a curve is a line such that the distance of any point P on the curve from the focus of the curve is a constant multiple of the distance of P from the directrix. This multiple is called the eccentricity of the curve. A circle however is a limiting case.

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.

How do you find the focus and directrix?

Focus & directrix of a parabola from the equation So the focus is (h, k + C), the vertex is (h, k) and the directrix is y = k – C.

How do you find the Directrix of a circle?

How do you define directrix?

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?

How to find the directrix, focus and vertex of a parabola y = ½ x2. The axis of the parabola is y-axis. Equation of directrix is y = -a. i.e. y = -½ is the equation of directrix.

How do you find the focus of an equation?

In order to find the focus of a parabola, you must know that the equation of a parabola in a vertex form is y=a(x−h)2+k where a represents the slope of the equation. From the formula, we can see that the coordinates for the focus of the parabola is (h, k+1/4a).