Ellipse

[laladida88]

3. Put the equation in standard from for an ellipse.
25x^2 +150x +9y^2 -8y =-9


I keep getting 1/4 (x +3) ^2 + 1/25 (y -2) ^2 =1

?

proof?

 

[soroban]

Hello, laladida88!

I assume there is a typo in the equation.

3\(\displaystyle \text{3. Write in standard form: }\:25x^2 + 150x + 9y^2 - \color{green}{18}y \:=\:-9\)

We have:

.. \(\displaystyle 25(x^2 + 6x \qquad) + 9(y^2 - 2y \qquad) \;=\;\text{-}9\)


Complete the square:

. . \(\displaystyle \color{red}{25}(x^2 + 6x \color{red}{+ 9}) + \color{blue}{9}(y^2 - 2y \color{blue}{+ 1}) \;=\;\text{-}9 \color{red}{+ 225} \color{blue}{+ 9}\)


Factor:

. . \(\displaystyle 25(x+3)^2 + 9(y-1)^2 \;=\;225\)


Divide by 225:

. . \(\displaystyle \dfrac{(x+3)^2}{9} + \dfrac{(y-1)^2}{25} \;=\;1\)