Chapter 9, Problem 21RE

To determine

Calculate the standard form of the equation of the parabola.

Answer to Problem 21RE

The equation of the parabola is ${(x+6)}^2=-9(y-4)$ .

Explanation of Solution

Given:

It is given in the question that the graph is given below:

  

Concept Used:

In this, use the concept of parabola and a formula is ${(x-h)}^2=4p(y-k)$ .

Calculation:

Here, the parabola has its vertex at $(6,-4)$ . The vertical axis is $x=-6$ . Use the given points and the equation of a parabola with a vertical axis to find p.

  ${(x-h)}^2=4p(y-k)$

Now, find p:

  $\begin{array}{l}$ {(x-h)}^2=4p(y-k)$p=\frac{{(x-h)}^2}{4(y-k)}\end{array}$

Now, put all the given points:

  $\begin{array}{l}p=\frac{{(x-h)}^2}{4(y-k)}\\ p=\frac{{(0-(-6))}^2}{4(0-4)}\\ p=\frac{{(6)}^2}{4(-4)}\\ p=\frac{36}{-16}=-\frac{9}{4}\end{array}$

Now, put the above term in the equation:

  ${(x+6)}^2=-9(y-4)$ .

Conclusion:

The equation is ${(x+6)}^2=-9(y-4)$ .