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  x^2/25 +y^2/9 = 1

Step-by-step explanation:

You can think of an ellipse as a circle with a different scale factor in the x-direction than in the y-direction. When either dimension is stretched by a factor of k, the corresponding variable (v) is replaced by (v/k).

Here, the unit circle

  x^2 +y^2 = 1

is stretched by a factor of 3 vertically (in the y-direction) and a factor of 5 horizontally (in the x-direction). That means we can replace x with (x/5) and  y with (y/3) in the above equation to get ...

  (x/5)^2 +(y/3)^2 = 1

Traditionally, the denominator is written as a number, not a square, so the equation would be ...

  x^2/25 +y^2/9 = 1