# What Is An Equation Of A Parabola With The Given Vertex And Focus (-2 5) (-2 6)

What is an equation of a parabola with the given vertex and 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.

Furthermore, What is an equation of the parabola with vertex at the origin and focus (- 5 0?, Explanation: Focus is at (5,0) and vertex is at (0,0) . the equation of parabola is y2=4ax , a=5 is the focal distance (the distance from vertex to focus).

Finally,  How do you find the equation of a parabola with a focus and Directrix?, The process of obtaining the equation is similar, but it is more algebraically intensive. Given the focus (h,k) and the directrix y=mx+b, the equation for a parabola is (y – mx – b)^2 / (m^2 +1) = (x – h)^2 + (y – k)^2.

### What is the equation of the parabola with a vertex at (- 2 3?

equation of parabola can be expressed as, y=a(x−h)2+k where, (h,k) is the coordinate of vertex and a is a constant.

### What is the equation of the parabola with a vertex at (- 2 3 and a focus at (- 2 0?

Answer: The equation is (x + 2)² = -12(y – 3).

### How do you find the equation of a parabola given the vertex and a point?

In this equation, the vertex of the parabola is the point (h,k) . You can see how this relates to the standard equation by multiplying it out: y=a(x−h)(x−h)+ky=ax2−2ahx+ah2+k .

## How to find a parabola’s equation using its Vertex Form

1. Step 1: use the (known) coordinates of the vertex, (h,k), to write the parabola’s equation in the form: y=a(x−h)2+k. …
2. Step 2: find the value of the coefficient a by substituting the coordinates of point P into the equation written in step 1 and solving for a.

### What is the equation of a parabola with vertex and 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.

## Finding the Equation of a Parabola Given Focus and Directrix

1. Let (a,b) be the focus and let y=c be the directrix. …
2. Any point, (x0,y0) on the parabola satisfies the definition of parabola, so there are two distances to calculate:
3. Distance between the point (x0,y0) and (a,b) :
4. Distance between point (x0,y0) and the line y=c :
5. | y0−c |

## How to find a parabola’s equation using its Vertex Form

1. Step 1: use the (known) coordinates of the vertex, (h,k), to write the parabola’s equation in the form: y=a(x−h)2+k. …
2. Step 2: find the value of the coefficient a by substituting the coordinates of point P into the equation written in step 1 and solving for a.

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

Douglas K. 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 an equation of the parabola with vertex at the origin and focus (- 6 0?

y²=2px is his equation.

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

Given the focus (h,k) and the directrix y=mx+b, the equation for a parabola is (y – mx – b)^2 / (m^2 +1) = (x – h)^2 + (y – k)^2.

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

Douglas K. 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.

## How to find a parabola’s equation using its Vertex Form

1. Step 1: use the (known) coordinates of the vertex, (h,k), to write the parabola’s equation in the form: y=a(x−h)2+k. …
2. Step 2: find the value of the coefficient a by substituting the coordinates of point P into the equation written in step 1 and solving for a.

### How do you write an equation with only the vertex?

1. Vertex form of a quadratic equation is y=a(x-h)2+k, where (h,k) is the vertex of the parabola.
2. The vertex of a parabola is the point at the top or bottom of the parabola.
3. ‘h’ is -6, the first coordinate in the vertex.
4. ‘k’ is -4, the second coordinate in the vertex.
5. ‘x’ is -2, the first coordinate in the other point.

### What is an equation of the parabola with vertex at the origin and focus 0?

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.

### What is an equation of the parabola with vertex at the origin and focus (- 6 0?

y²=2px is his equation.

## Finding the Equation of a Parabola Given Focus and Directrix

1. Let (a,b) be the focus and let y=c be the directrix. …
2. Any point, (x0,y0) on the parabola satisfies the definition of parabola, so there are two distances to calculate:
3. Distance between the point (x0,y0) and (a,b) :
4. Distance between point (x0,y0) and the line y=c :
5. | y0−c |

### How do you find the equation of a 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.

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