The standard equation of a parabola with focus (2,-3) and directrix x=6 is

Options

A. `(y+3)^(2)=8(x-2)`
B. `(y+3)^(2)=-8(x-4)`
C. `(x-2)^(2)=8(y+3)`
D. `(x+2)^(2)=-8(y-3)`

Explanation

To find the standard equation of a parabola with a given focus and directrix, we can follow these steps:

### Step 1: Understand the Definitions
The definition of a parabola states that it is the set of all points that are equidistant from a fixed point (the focus) and a fixed line (the directrix). In this case, the focus is (2, -3) and the directrix is the line x = 6.

### Step 2: Set Up the Equation
Let (x, y) be any point on the parabola. The distance from the point (x, y) to the focus (2, -3) can be calculated using the distance formula:

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