So i had a trig test today, and my teacher marked off a problem, and ive reviewed it plenty of times, but cant seem to figure out what i did wrong. Could someone please help me with this, i am simply converting to standard form of an ellipse/hyperbola. The equation is x^2 + 4y^2 +2x +16y = -1 .

I believe that my answer was something like ((x+1)^2)/4 + ((y+2)^2)/1 = 1 .

I am not possitive if that was my exact answer, but i am sure the problem is exact. I think i got it right and just neglected to show some valuable piece of work, and my strict math teacher counted it off. Thx in advance for the help, and i appologize for not using latex, i was in a hurry.

when you completed the squares you neglected to properly add the (b/2)^2 terms to the rhs of the equation it should be equal to 4

No, you did hnot get it right! I think your error was that when you "completed the square" for the y terms you added "4" on the right hand side but forgot that it should be multiplied by the 4 multiplying (x+1)^2. You should have had 16 on the right hand side, not 4, and then, dividing the entire equation by 16,

(x+1)^2/16+ (y+2)^2/4= 1.

 

By the way, why did you title this "standard form for a circle"?

thx for the reply, turns out i had it right on my paper, when i tried to remember what i put, i did it mentally and for got to multiply the 4, but i had it right on the test, just forgot to show how i found my c value to graph it, but thanks for the help anyways. I titled it "standard form for a circle because thats what i was trying to find and i was in a hurry lol.