Question

4x2+9y2-8x+36y-31=0​

Answer 1

Answer:

The centre is at (1,2)

The vertices are at (12,2),(32,2),(1,2⋅13) and (1,1⋅23)

The foci are at (1−√56,2) and (1+√56,2)

The eccentricity is (√56)

Explanation:

Rearrange the elements to get the standard form of an ellipse

(x−h)2a2+(y−k)2b2=1 where (h,k) is the centre and a and b are the semi-minor and semi-major axes respectively.

So in this example

4x2−8x+9y2−36y+4=0

Using the method of completing squares

4(x2−2x)+9(y2−4y)+4=0

4(x−1)2