Given the ellipse 8x^2 + y^2 + 80x - 6y + 193 = 0 find: a) The Center C
If you have more than one question, you need to make separate posts.
To find the center of an ellipse, it needs to be put into standard form. This means that you need complete the square for both the x and y coordinates.
`8x^2+y^2+80x-6y+193=0` collect terms for x and y
`8x^2+80x+y^2-6y+193=0` factor 8 from x terms
`8(x^2+10x)+y^2-6y+193=0` add and subtract to complete the square
`8(x^2+10x+25-25)+y^2-6y+9-9+193=0` arrange perfect squares
`8(x+5)^2-8(25)+(y-3)^2-9+193=0` collect constants
`8(x+5)^2+(y-3)^2=16` divide by 16
The centre of the ellipse is at (-5,3).