Question

Which of the following is the equation for the graph shown?a. x^2/144+y^2/95=1b. x^2/144-y^2/95=1c. x^2/95+y^2/144=1d. x^2/95-y^2/144=1

Answer 1

e follSOLUTION

Given the question in the image, the following are the solution steps to answer the question

STEP 1: Write the general equation of an ellipse

`(\mleft(x-h\mright)^2)/(a^2)+\frac{(y-h)^2}{b^2^{}}=1`

STEP 2: Identify the parameters

the length of the major axis is 2a

the length of the minor axis is 2b

`\begin{gathered} 2a=24,a=(24)/(2)=12 \\ 2b=20,b=(20)/(2)=10 \end{gathered}`

STEP 3: Get the equation of the ellipse

`\begin{gathered} By\text{ substitution,} \\ ((x-h)^2)/(a^2)+((y-h)^2)/(b^2)=1 \\ ((x-0)^2)/(12^2)+((y-0)^2)/(10^2)=1=(x^2)/(144)+(y^2)/(100)=1 \end{gathered}`

STEP 4: Pick the nearest equation from the options,

Hence, the equation of the ellipse in the image is given as:

`(x^2)/(144)+(y^2)/(95)=1`

OPTION A