Recall that the major axis is "a + a" or 2a, whilst the minor axis is "b + b" or 2b.
so if the major axis is 30, then a = 15, and if the minor one is 14, b = 7.
![\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x-{{ h}})^2}{{{ a}}^2}+\cfrac{(y-{{ k}})^2}{{{ b}}^2}=1 \qquad \begin{cases} center\ ({{ h}},{{ k}})\\ vertices\ ({{ h}}\pm a, {{ k}}) \end{cases}\\\\ -------------------------------\\\\ \textit{we know that } \begin{cases} a=\frac{30}{2}\\ b=\frac{14}{2}\\ h=-9\\ k=-7 \end{cases}\implies \cfrac{[x-(-9)]^2}{15^2}+\cfrac{[y-(-7)]^2}{7^2}=1 \\\\\\ \cfrac{(x+9)^2}{225}+\cfrac{(y+7)^2}{49}=1](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bellipse%2C%20horizontal%20major%20axis%7D%0A%5C%5C%5C%5C%0A%5Ccfrac%7B%28x-%7B%7B%20h%7D%7D%29%5E2%7D%7B%7B%7B%20a%7D%7D%5E2%7D%2B%5Ccfrac%7B%28y-%7B%7B%20k%7D%7D%29%5E2%7D%7B%7B%7B%20b%7D%7D%5E2%7D%3D1%0A%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0Acenter%5C%20%28%7B%7B%20h%7D%7D%2C%7B%7B%20k%7D%7D%29%5C%5C%0Avertices%5C%20%28%7B%7B%20h%7D%7D%5Cpm%20a%2C%20%7B%7B%20k%7D%7D%29%0A%5Cend%7Bcases%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A%5Ctextit%7Bwe%20know%20that%20%7D%0A%5Cbegin%7Bcases%7D%0Aa%3D%5Cfrac%7B30%7D%7B2%7D%5C%5C%0Ab%3D%5Cfrac%7B14%7D%7B2%7D%5C%5C%0Ah%3D-9%5C%5C%0Ak%3D-7%0A%5Cend%7Bcases%7D%5Cimplies%20%5Ccfrac%7B%5Bx-%28-9%29%5D%5E2%7D%7B15%5E2%7D%2B%5Ccfrac%7B%5By-%28-7%29%5D%5E2%7D%7B7%5E2%7D%3D1%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B%28x%2B9%29%5E2%7D%7B225%7D%2B%5Ccfrac%7B%28y%2B7%29%5E2%7D%7B49%7D%3D1)
so if the major axis is 30, then a = 15, and if the minor one is 14, b = 7.
Here are two steps from the derivation of the quadratic formula
2 answers:
Answer:
C
Step-by-step explanation:
Completing the square means
adding ( half the coefficient of the x- term )² to both sides, that is
( )² is added to both sides
Answer:
completing the square
Step-by-step explanation:
Two steps are given for the derivative of quadratic formula.
In completing the square method, we take the coefficient of x and then divide it by 2 and then square it.
Here coefficient of x is b/a
divide by 2 becomes
Then we square it
becomes
So, the competing the square took place between the first and second step
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