Question

Find the equation of the ellipse with the following properties.

The ellipse with foci at (4, 0) and (-4, 0); y-intercepts (0, 3) and (0, -3)

Answer 1

Explanation:

The equation of the ellipse

`\displaystyle\\\boxed {(x^2)/(a^2) +(y^2)/(b^2) =1}`

`F^2=a^2-b^2`

Given: F₁(-4,0) F₂(4,0) b₁(0,-3) b₂=(0,3)

`\displaystyle\\a^2=F^2+b^2\\\\a^2=4^2+3^2\\\\a^2=16+9\\\\a^2=25\\\\a_(1,2)=б5\\\\So,\ a_1(-5,0)\ \ \ \ a_2(5,0)\\\\Thus,\ (x^)/((б5)^2) +(y^2)/((б3)^2) =1\\\\(x^2)/(25)+(y^2)/(9) =1\ \ \ \ -\ the\ equation \ of\ the\ ellipse`