How do you classify the conic sectin and write its equation in standard form?

Question

9x^2 + 36y^2 + 54x - 144y - 99 = 0

i dont really understand

could u explain?

Answer 1

First group together like terms and complete the square. 9(x^2+6x+9)+36(y^2-4y-4)=36
9(x+3)^2+36(y-2)^2=36
(x+3)^2 / (4)^2+(y-2)^2 / (3)^2 = 1
The standard equations for conics are given
http://jwilson.coe.uga.edu/EMT668/EMT668.Student.Folders/HeadAngela/InstrucUnit/instrucunit
Thus by looking at this one can see its an ellipse. For other conic sections, try to rearrange like terms and then complete the square for each quadratic of x and y. This should help out a lot.

Answer 2

That's an ellipse

9*(x+3)^2 - 81 + 36*(y - 2)^2 - 144 - 99 = 0
9*(x+3)^2 + 36*(y - 2)^2 = 18^2
(x+3)^2 / 6^2 + (y-2)^2 / 3^2 = 1

Answer 3

ellipse