Answer:
Not sure
Step-by-step explanation:
Parallel lines have the same slope. The equation of the parallel line is therefore:
y = x + b
Plug in the values you are given to find b:
2 = -3 + b
b = 5
An ellipse (oval shape) is expressed by the following equation:
![\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2}=1](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28x-h%29%5E2%7D%7Ba%5E2%7D%20%2B%20%5Cfrac%7B%28y-k%29%5E2%7D%7Bb%5E2%7D%3D1%20)
where h is the x coordinate of the center and k is the y coordinate of the center. Furthermore, a is the horizontal distance from the center, and b is the vertical distance from the center. Lastly, c is the distance from the center to one of the foci (they are spaced apart equally).
We can find the foci by using
![a^2 - b^2 = c^2](https://tex.z-dn.net/?f=a%5E2%20-%20b%5E2%20%3D%20c%5E2)
36 - 11 =
![c^2](https://tex.z-dn.net/?f=c%5E2)
![c = \sqrt{25} = 5](https://tex.z-dn.net/?f=c%20%3D%20%20%5Csqrt%7B25%7D%20%20%3D%205)
Since the k value in this case is 0, the y value of both foci are 0. Also, since h and k are both 0, we know the center of the ellipse is at the origin.
So the foci are (-5, 0) and (5, 0)
Hope this helps :)
To find the final term to compete the square you need to divide the 'x' term by 2 then square it
![x^2 +18x + = 44+ \\ x^2+18x+( \frac{18}{2} )^2=44+( \frac{18}{2} )^2 \\ x^2+18x+9^2=44+9^2 \\ x^2+18x+81=44+81 \\ (x+9)^2=125](https://tex.z-dn.net/?f=x%5E2%20%2B18x%20%2B%20%3D%2044%2B%20%5C%5C%20x%5E2%2B18x%2B%28%20%5Cfrac%7B18%7D%7B2%7D%20%29%5E2%3D44%2B%28%20%5Cfrac%7B18%7D%7B2%7D%20%29%5E2%20%5C%5C%20x%5E2%2B18x%2B9%5E2%3D44%2B9%5E2%20%5C%5C%20x%5E2%2B18x%2B81%3D44%2B81%20%5C%5C%20%28x%2B9%29%5E2%3D125)
- equivalent equation