What is the equation of the parabola with focus at 0 2 and Directrix Y =- 2?

y = 1/8×2
y = 1/8×2 is the equation of a parabola with focus (0, 2) and directrix y = -2.

What is equation of a parabola with focus 0 4 and Directrix Y 2?

The equation y = (x2/4) + 3 represents a parabola with a focus of (0, 4) and a directrix of y = 2.

Which is the standard form of the equation of a parabola with a focus of 0 and its vertex at the origin?

The equations of parabolas with vertex (0,0) are y2=4px y 2 = 4 p x when the x-axis is the axis of symmetry and x2=4py x 2 = 4 p y when the y-axis is the axis of symmetry. These standard forms are given below, along with their general graphs and key features.

What are the coordinates of the focus of the parabola 0 2?

The focus of a parabola is located at (0,-2). The directrix of the parabola is represented by y = 2.

How do you find the equation of a parabola with focus?

If you have the equation of a parabola in vertex form y=a(x−h)2+k, then the vertex is at (h,k) and the focus is (h,k+14a). Notice that here we are working with a parabola with a vertical axis of symmetry, so the x-coordinate of the focus is the same as the x-coordinate of the vertex.

Which of the following is the equation for a parabola with a focus at 0 4 and a Directrix at Y − 4?

Summary: The equation of the parabola with a focus at (0, -4) and a directrix of y = 4 is x2 + 16y = 0.

What is the equation of the parabola?

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.

Which equation represents a parabola with the focus?

How do you find the focus of a parabola in standard form?

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).

What is the equation of the parabola with focus(a B and directrix Y=C)?

This equation in ( x 0 , y 0 ) is true for all other values on the parabola and hence we can rewrite with ( x , y ) . Therefore, the equation of the parabola with focus ( a , b ) and directrix y = c is. ( x − a ) 2 + b 2 − c 2 = 2 ( b − c ) y. Example:

How do you find the distance of a parabola?

Any point, ( x 0, y 0) on the parabola satisfies the definition of parabola, so there are two distances to calculate: To find the equation of the parabola, equate these two expressions and solve for y 0 . Find the equation of the parabola in the example above. Distance between the point ( x 0, y 0) and ( a, b) :

What are the four possible orientations of the parabola?

The four such possible orientations of the parabola are explained in the table below: Equation Formulas y 2 = 4ax Focus = (a, 0); a > 0 Directrix: x = -a y 2 = -4ax Focus = (-a, 0); a < 0 Directrix: x = a x 2 = 4ay Focus = (0, a); a > 0 Directrix: y = -a x 2 = -4ay Focus = (0, -a); a < 0 Directrix: y = a

How do you find the axis of symmetry of a parabola?

Example 1: Find the coordinates of the focus, axis, the equation of the directrix and latus rectum of the parabola y 2 = 12x. to the right. Also, the axis of symmetry is along the positive x-axis. Focus of the parabola is (a, 0) = (3, 0). Equation of the directrix is x = -a, i.e. x = -3 or x + 3 = 0.