## What is the equation of the directrix of the parabola?

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 Latus of a parabola?

Latus Rectum of a Parabola The latus rectum of parabola can also be understood as the focal chord which is parallel to the directrix of parabola. The length of latus rectum for a standard equation of a parabola y2 = 4ax is equal to LL’ = 4a. The endpoints of the latus rectum of a Parabola are (a, 2a), (a, -2a).

**How do u 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 .

**How do you find the Directrix and focus of an equation?**

The standard form is (x – h)2 = 4p (y – k), where the focus is (h, k + p) and the directrix is y = k – p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y – k)2 = 4p (x – h), where the focus is (h + p, k) and the directrix is x = h – p.

## What are the 4 types of parabola?

Four Common Forms of a Parabola:

Form: | y2 = 4ax | x2 = – 4ay |
---|---|---|

Vertex: | (0, 0) | (0, 0) |

Focus: | (a, 0) | (0, -a) |

Equation of the directrix: | x = – a | y = a |

Equation of the axis: | y = 0 | x = 0 |

### What is a parabola Class 10?

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point, which is the focus, and from a fixed straight line, which is known as the directrix. The set of all points in a plane that are equidistant from a fixed line and a fixed point in the plane is a parabola.

**How do I find the axis of symmetry of a parabola?**

The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a .

**WHAT IS A in Y 2 4ax?**

The equation y2 = – 4ax (a > 0) represents the equation of a parabola whose co-ordinate of the vertex is at (0, 0), the co-ordinates of the focus are (- a, 0), the equation of directrix is x = a or x – a = 0, the equation of the axis is y = 0, the axis is along negative x-axis; the length of its latus rectum is 4a and …

## What is the locus of a parabola?

The Greeks defined the parabola using the notion of a locus. A locus is a set of points satisfying a given condition. These points will generally lie on some curve. For example, the circle with centre O and radius r is the locus of a point P moving so that its distance from the point O is always equal to r.

### How do you find the equation of the locus?

Let us assume that P(x,y) P ( x , y ) is a point on the given locus. The above equation can be converted to the form x2a2+y2b2=1 x 2 a 2 + y 2 b 2 = 1 and hence it represents an ellipse. Thus, the equation of locus is, 36×2+20y2=45 36 x 2 + 20 y 2 = 45 which is an ellipse.