Question

Write the following equation in standard form and identify the type of conic:

9y^2 - 4x^2 + 8x + 18y + 41 = 0

Answer 1

9y^2 - 4x^2 + 8x + 18y + 41 = 0
4x^2 - 8x - 9y^2 - 18y - 41 = 0
4(x^2 - 2x + ......) - 9(y^2 + 2y + .... ) = 41
let's "complete these squares"
4(x^2 - 2x + 1) - 9(y^2 + 2y + 1 ) = 41 + 4 - 9
4(x-1)^2 - 9(y+1)^2 = 36
divide by 36

(x-1)^2/9 - (y+1)^2/4 = 1

If you are studying conics you should now be able to identify the conic and state its properties.