The centre of an ellipse is at (0, 0), major axis is on the y-axis. If the ellipse passes through (3, 2) and (1, 6), then what is its eccentricity ?

Concept:

The equation of ellipse with centre (0,0) is of the form, 

For an ellipse  with y-axis as major axis, the eccentricity = 

Calculation:

Given: The centre of an ellipse is at (0, 0), major axis is on the y-axis and the ellipse passes through (3, 2) and (1, 6).

Let the equation of the ellipse be 

(3,2) and (1,6) lies on the ellipse

⇒  and 

⇒  __(i)

and  __(ii)

Subtracting (i) from (ii),

⇒ 

 ⇒ 32a²​ = 8b²

⇒ 4a² = b²

Put in (i) 

⇒ 

⇒ a² = 10

⇒ b² = 4 × 10 = 40 

So, the equation of the ellipse will be 

Now for the ellipse , the eccentricity of the ellipse is given by,

⇒ 

⇒ Eccentricity = 

∴ The correct option is (1).