Question

Determine the type and key parts of the graph of the second equation

Answer 1

`\begin{gathered} \left(h,\:k\right)=\left(0,\:0\right),\:a=3,\:b=6 \\ major\text{ axis;vertical} \\ minoraxis;horizontal \end{gathered}`

Step-by-step explanation

The second equation;

`(x^2)/(9)+(y^2)/(36)=1`

It is an Elipse.

Ellipse standard equation;

`(\left(x-h\right)^2)/(a^2)+(\left(y-k\right)^2)/(b^2)=1`

Rewrite the given equation in the form of the standard equation;

Hence, we have;

`(\left(x-0\right)^2)/(3^2)+(\left(y-0\right)^2)/(6^2)=1`

Therefore the ellipse properties are;

`\left(h,\:k\right)=\left(0,\:0\right),\:a=3,\:b=6`

Major axis is;

`\begin{gathered} 2a \\ =2*6=12 \end{gathered}`

Minor axis is;

`\begin{gathered} 2b \\ =2*3=6 \end{gathered}`