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.

## Frequently Asked Question:

### 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 do you find the equation of a parabola with only the vertex?

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

- 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. …
- 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.

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

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

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

### How do I find the equation of a parabola?

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

- 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. …
- 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 do you find the equation of a parabola with only the vertex?

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

- 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. …
- 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?

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

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

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

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