Question

Find an equation of the lips having major axis of length and foci

Answer 1

Given:

Major axis = 10

Foci at (-1,0) and (-7,0)

Find-: Equation of ellipse.

Sol:

The major axis length is 10.

That mean:

`\begin{gathered} 2a=10 \\ \\ a=(10)/(2) \\ \\ a=5 \end{gathered}`

Distance between two foci is:

`\begin{gathered} D=|-7-(-1)| \\ \\ D=|-7+1| \\ \\ D=6 \end{gathered}`

So,

`\begin{gathered} 2ae=6 \\ \\ ae=(6)/(2) \\ \\ ae=3 \\ \\ e=(3)/(5) \end{gathered}`

The value of "b" is:

`\begin{gathered} b^2=a^2(1-e^2) \\ \\ b^2=25(1-(9)/(25)) \\ \\ b^2=25-9 \\ \\ b^2=16 \end{gathered}`

Center of ellipse = Midpoint of foci

`\begin{gathered} =((-1+(-7))/(2),(0+0)/(2)) \\ \\ =(-4,0) \end{gathered}`

Hence, the equation of the ellipse is:

`((x+4)^2)/(25)+(y^2)/(16)=1`