Equation of an Ellipse:
The general equation of an ellipse centered at the origin is given by:
(x^2/a^2) + (y^2/b^2) = 1

Finding the Eccentricity:
The eccentricity (e) of an ellipse is a measure of how "elongated" the ellipse is. It is defined as the ratio of the distance between the center of the ellipse and one of its foci (c) to the semi-major axis (a).
e = c/a

Given that the eccentricity of the ellipse is sqrt(2/5), we can express it as:
sqrt(2/5) = c/a

Squaring both sides of the equation, we get:
2/5 = (c/a)^2

Multiplying both sides by 5, we have:
2 = 5(c/a)^2

Simplifying further:
(c/a)^2 = 2/5

Taking the square root of both sides, we obtain:
c/a = sqrt(2/5)

Finding the Distance from the Center to the Focus:
Since the eccentricity is defined as the ratio of the distance between the center and a focus to the semi-major axis, we can express it as:
e = c/a

Rearranging the equation, we can solve for c:
c = ea

Substituting the given value of the eccentricity (sqrt(2/5)) and the distance from the center to a focus (c), we have:
c = sqrt(2/5) * a

Substituting the Given Point:
The given point (-3,1) lies on the ellipse. Substituting these coordinates into the equation of an ellipse, we get:
((-3)^2/a^2) + (1^2/b^2) = 1
9/a^2 + 1/b^2 = 1

Simplifying the Equation:
Using the relationship between the eccentricity and the semi-major axis, we can substitute the value of c in terms of a:
(2/5) * a^2 + 1/b^2 = 1

Multiplying both sides by 5 to eliminate the fraction, we have:
2a^2 + 5/b^2 = 5

Multiplying both sides by b^2 to eliminate the fraction, we obtain:
2a^2b^2 + 5 = 5b^2

Rearranging the equation, we get:
2a^2b^2 - 5b^2 + 5 = 0

Conclusion:
The equation of the ellipse passing through the point (-3,1) with an eccentricity of sqrt(2/5) is given by:
2a^2b^2 - 5b^2 + 5 = 0, where a is the semi-major axis and b is the semi-minor axis of the ellipse.