3x^2+y^2+6x-8y-11=0

Question

Find centre and endpoints of the both axes

Answer 1

In order to find the answer you need to complete the square in the x and the y variable. So you need to add and subtract the correct numbers as follows

3x^2+y^2+6x-8y=11 same as 3(x^2+2x+1)+(y^2-2(4)y+16)=30 same as 3(x+1)^2+(y-4)^2=30 and it is clear now that you have an ellipse.