Answer:
Equation of the Ellipse
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given that the equation
x² + 2 x + 2y² - 12 y +11 = 0
⇒ x² + 2 x + 1 - 1 + 2(y² - 6 y )+ 11 = 0
x² + 2 x + 1 - 1 + 2(y² - 2(3) y+9-9 )+ 11 = 0
⇒ x² + 2 x + 1 - 1 + 2(y² - 2(3 y ) + 3²- 3² ) + 11 = 0
By using (a +b)² = a² + 2 a b + b²
(a -b)² = a² - 2 a b + b²
<u><em>Step(ii):-</em></u>
x² + 2 x + 1 - 1 + 2(y² - 2(3 y ) + 3²- 3² ) + 11 = 0
⇒ ( x+1)² +2( y-3 )² - 1 - 2(9) +11 =0
⇒ ( x+1)² +2( y-3 )² - 8 =0
( x+1)² +2( y-3 )² = 8
Dividing '8' on both sides , we get
![\frac{(x+1)^{2} }{8} + \frac{2(y-3)^{2} }{8} = 1](https://tex.z-dn.net/?f=%5Cfrac%7B%28x%2B1%29%5E%7B2%7D%20%7D%7B8%7D%20%2B%20%5Cfrac%7B2%28y-3%29%5E%7B2%7D%20%7D%7B8%7D%20%3D%201)
![\frac{(x+1)^{2} }{8} + \frac{(y-3)^{2} }{4} = 1](https://tex.z-dn.net/?f=%5Cfrac%7B%28x%2B1%29%5E%7B2%7D%20%7D%7B8%7D%20%2B%20%5Cfrac%7B%28y-3%29%5E%7B2%7D%20%7D%7B4%7D%20%3D%201)
This equation represents the Ellipse
Answer:
The answer is Option 1
Step-by-step explanation:
= approximately 3.16
3.16 is in between 3 and 3.5
Answer:
-2x^3 - 3x^2 -8x + 4 should be added
Step-by-step explanation:
Here, we want to know what should be added to the expression to get 0
What we should do in this case is to simply negate the values we have in the expression already
Adding the negated values will give 0
So, we have that;
-2x^3 - 3x^2 -8x + 4
If I am correct, the answer should be D. If you need further explanation, I can supply you with that as well.
Answer:
![\large\boxed{D)\ y=\dfrac{1}{5}x+5}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7BD%29%5C%20y%3D%5Cdfrac%7B1%7D%7B5%7Dx%2B5%7D)
Step-by-step explanation:
The slope-intercept form of an equation of a line:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
m - slope
b - y-intercept
The formula of a slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
From the graph we have the y-intercept (0, 5) ⇒ b = 5
and the other point (5, 6).
Put the coordinates of the point to the formula of a slope:
![m=\dfrac{6-5}{5-0}=\dfrac{1}{5}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B6-5%7D%7B5-0%7D%3D%5Cdfrac%7B1%7D%7B5%7D)
Finally we have the equation:
![y=\dfrac{1}{5}x+5](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B1%7D%7B5%7Dx%2B5)