Question

find the directrix of the parabola defined by the equation $(y - 7)^2 = 40(x - 9)$. answer attempt 2 out of 2 directrix: $x=7$

Explanation:

Step1: Identify the standard form of the parabola

The standard form of a parabola that opens to the right or left is \((y - k)^2 = 4p(x - h)\), where \((h,k)\) is the vertex.
For the given equation \((y - 7)^2 = 40(x - 9)\), we have \(h = 9\), \(k = 7\), and \(4p=40\).

Step2: Solve for \(p\)

From \(4p = 40\), we get \(p=\frac{40}{4}=10\).

Step3: Find the directrix

For a parabola of the form \((y - k)^2 = 4p(x - h)\) (opens to the right when \(p>0\)), the directrix is given by the equation \(x=h - p\).
Substitute \(h = 9\) and \(p = 10\) into \(x=h - p\), we have \(x=9-10=- 1\).

Answer:

\(x=-1\)