The equation of the parabola with the given vertex and directrix in vertex form is y = (1/16)( x + 5 )² - 9.
Hence, option C is the correct answer.
<h3>What is the equation of the parabola?</h3>
Given the data in the question;
- Vertex of the parabola: ( -5, -9 )
- h = -5
- k = -9
- Directrix of the parabola: y = -13
To find the equation, we use the equation of the parabola that opens up or down since the directrix ( y = -13 ) is vertical.
The equation is expressed as;
( x - h )² = 4p( y - k )
First, we find the distance from the focus to the vertex.
|p| is the distance rom the focus to the vertex and from the vertex to the directrix.
p = -9 + 13
p = 4
We substitute the values into the equation;
( x - h )² = 4p( y - k )
( x - (-5) )² = 4(4)( y - (-9) )
( x + 5 )² = 16( y + 9 )
Multiply both side by 1/16
(1/16)( x + 5 )² = y + 9
Make y the subject of the formula
(1/16)( x + 5 )² - 9 = y
y = (1/16)( x + 5 )² - 9
The equation of the parabola with the given vertex and directrix in vertex form is y = (1/16)( x + 5 )² - 9.
Hence, option C is the correct answer.
Learn more about equation of parabola here: brainly.com/question/21685473
#SPJ1
Answer:
The same measure of what? The angle of the arc or the length? If it is the same angle, then it is similar. If it is the same length and angle then it is congruent.
Step-by-step explanation:
Step-by-step explanation:
![4 5\div 15 = 3](https://tex.z-dn.net/?f=4%205%5Cdiv%2015%20%3D%203)
![\frac{45}{15} = 3](https://tex.z-dn.net/?f=%20%5Cfrac%7B45%7D%7B15%7D%20%20%3D%203)
![\frac{15 + 15 + 15}{15} = 3](https://tex.z-dn.net/?f=%20%5Cfrac%7B15%20%2B%2015%20%2B%2015%7D%7B15%7D%20%20%3D%203)
![\frac{3(15)}{15} = 3](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%2815%29%7D%7B15%7D%20%20%3D%203)
![3 \times \frac{15}{15} = 3](https://tex.z-dn.net/?f=3%20%5Ctimes%20%20%5Cfrac%7B15%7D%7B15%7D%20%20%3D%203)
![3 \times 1 = 3](https://tex.z-dn.net/?f=3%20%5Ctimes%201%20%3D%203)
![3 = 3](https://tex.z-dn.net/?f=3%20%3D%203)
Choose two points on the hexagon that form a line. Plug the numbers into the distance formula and work it out. Because all the sides are equal, you only need to do this once. Hope this helped!
Answer:
The first one...A
Step-by-step explanation: