What is an equation of the parabola with vertex at the origin and Directrix?

The standard form of the parabola is y2=4ax , giving a parabola with its axis parallel to the x -axis, vertex at the origin, focus (a,0) and directrix x=−a . So in your case a=2 , giving y2=4ax .

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

(x – h)2 = 4p (y – k), where (h, k) is the vertex, the focus is (h, k + p), and the directrix is y = k – p.

What is the equation of parabola whose vertex is at the origin and focus is at 0 2 3?

(iii) having vertex at origin and focus at (0,2) (i) Here, focus S(0,-3) and directrix y=3 are at same distance from origin is vertex of the parabola and parabola opens downwards. So, we consider equation x2=-4ay. So, equation of parabola is y2=-12x.

What is vertex at the origin?

The vertex is the midpoint between the directrix and the focus. The line segment that passes through the focus and is parallel to the directrix is called the latus rectum, also called the focal diameter. The endpoints of the focal diameter lie on the curve.

What is the standard equation of a parabola with vertex at HK?

To graph parabolas with a vertex (h,k) other than the origin, we use the standard form (y−k)2=4p(x−h) ( y − k ) 2 = 4 p ( x − h ) for parabolas that have an axis of symmetry parallel to the x-axis, and (x−h)2=4p(y−k) ( x − h ) 2 = 4 p ( y − k ) for parabolas that have an axis of symmetry parallel to the y-axis.

What is the equation of the parabola in vertex form with vertex at 2 4 and Directrix Y?

The focus (-2, -4) is in the third quadrant and is below the directrix y = 2, so the parabola is inverted, and the sign of p is negative. The distance between the focus (-2, -4) and the directrix y = 2 along the x-coordinate x = -2 is |p| = 2 – (-4) = 6.

Which is the equation of a parabola with vertex at the origin and focus at 0 1?

Use the form y=a(x−h)2+k where (h,k)=(0,0) and a=14f where f is the signed vertical distance from the vertex to the focus, -2.

What is the standard equation of a parabola with vertex at origin and focus at 0 4 )?

A General Note: Standard Forms of Parabolas with Vertex (0, 0)

Axis of Symmetry	Equation	Focus
x-axis	y2=4px	(p, 0)
y-axis	x2=4py	(0, p)

What is the equation of a parabola when the vertex at H K and the axis of symmetry on Y axis?

A General Note: Standard Forms of Parabolas with Vertex (h, k)

Axis of Symmetry	Equation	Focus
y=k	(y−k)2=4p(x−h)	(h+p, k)
x=h	(x−h)2=4p(y−k)	(h, k+p)