Question

how do i get the center, vertices, foci, and eccentricity of 9x^2+4y^2-36x+8y_31=0?

Answer 1

it looks like the equation for a circle or ellipse

Answer 2

(9x^2 -36x +n) + (4y^2 +8y +m) = 31 +n+m

complete the squares to find n and m

Answer 3

n = (36/2)^2 m=(8/2)^2

(9x^2 -36x +18^2) + (4y^2 +8y + 4^2) = 31+18^2+4^2

Answer 4

9(x^2 -4x + 9^3) + 4(y^2 +2y + 4) = 371.... if i did it right in me head

Answer 5

(3x - 18)^2 + (2y +4)^2 = 371

3(x-6)^2 + 2(y+2)^2 = 371

is what I ge so far

Answer 6

divide evertyhing by 371 and see what you can work out I guess...

Answer 7

and dont do stupid mistakes like I did..... that 3 and 2 dont get pulled out....

Answer 8

9(x^2 -4x + 9^3) + 4(y^2 +2y + 4) = 371 is the correct way...

solve your quadratics to get 2 solutions.....

Answer 9

im gonna get it one way or another..... ignore that 9^3 flub...

9(x^2 -4x + 36) + 4(y^2 +2y + 4) = 371