Question

3)determine if the foci for the following ellipse are correct and explain your reasoning 7x2 + 8y2 = 30; foci: (sqrt11, 0), (-sqrt11, 0)

Answer 1

The foci for the following ellipse are incorrect

Explanation:

Given equation:
`7x^2+8y^2=30`

Divide whole equation by 30

So,
`(x^2)/((30)/(7))+(y^2)/((30)/(8))=1`

General equation of ellipse:
`((x-h)^2)/(a^2)+((y-k)^2)/(b^2)`

On comparing
`a =(30)/(7)`

`b = (30)/(8)\\c^2=a^2-b^2\\c=√(a^2-b^2)\\c=\sqrt{((30)/(7))^2-((30)/(8))^2}\\c=(15√(15))/(28)`

So,the foci for the following ellipse are incorrect