Question

write the equation in standard form for the ellipse:

16x^2+48x+4y^2-20y+57=0

this is the answer that i got

4(x+3/2)^2 + (y-5/2)^2 = 1

im not sure if the 4 is suppose to be there

Answer 1

It's correct

Answer 2

but doesn't the denominators needs to be different?

Answer 3

4(x+3/2)^2 + (y-5/2)^2 = 1
=> 4(2x+3)^2 + (2y-5)^2 = 4

Answer 4

your answer was correct , but there are some modification ,just take LCM through out and take the denominator to the right hand side

Answer 5

for an ellipse the right hand side must be 1

Answer 6

if you don't like the 4 then move it to the denominator as (1/2)^2

Answer 7

(x+3/2)^2/.5^2 + (y-5/2)^2 = 1

and technically the denominators don't have to be different, because a circle is also an ellipse