# What is the equation in standard form of the parabola with a focus at (42,-31) and a directrix of y= 2?

##### 2 Answers

#### Explanation:

Please observe that the directrix is a horizontal line

Therefore, the parabola is the type that opens upward or downward; the vertex form of the equation for this type is:

Where

The x coordinate of the vertex is the same as the x coordinate of the focus:

Substitute

The y coordinate of the vertex is halfway between the directrix and the focus:

Substitute

The equation to find the value of

Substitute

Simplify the fraction:

Expand the square:

Distribute the fraction:

Combine like terms:

#### Explanation:

We will solve this **Problem** using the following **Focus-Directrix**

**Property (FDP)** of the **Parabola.**

**FDP :** Any point on a **Parabola** is **equidistant** from the

**Focus** and the **Directrix.**

Let, the point

the **Focus** and the **Directrix** of the **Parabola, say S.**

Let, **General Point.**

Then, using the **Distance Formula,** we have, the distance,

Knowing that the

By **FDP,**

**Standard Form,**

reads,

as **Respected Douglas K. Sir** has already derived!

**Enjoy Maths.!**