Question

are the following curves both circles about the origin? 16y^2-400+25x^2=0 and 16x^2-144=9y^2

Answer 1

circles around the origin have this form

\[x^2+y^2=r^2\]

Answer 2

when i put both of these into a simplified form they are such: 25x^2+16y^2=400 and 16x^2-9x^2=144. these do form the equation you supplied but i wish to know if it valid as both the x and y have values attached to them and are not simply x^2 and y^2

Answer 3

Help?

Answer 4

I have been told that the first one is a elipses and that the second one is a hyperbola how are these found?

Answer 5

\[16y^2-400+25x^2=0\]\[16y^2+25x^2=400\]\[\frac{16}{25}y^2+x^2=16\]\[\frac{16}{25}y^2+x^2=4^2\]
we see the first equation cannot be made into the form of a circle , because the x and y scale differently in the equation,

Answer 6

thank you very much.

Answer 7

the first equation is centered at the origin but is it an ellipse not a circle

Answer 8

the second equation\[16x^2-144=9y^2\]can be rearranged to
\[16x^2-9y^2=144\]

is this the equation of a circle?

Answer 9

not only do x and y scale differently, but one is negative compared to the other

this is a hyperboloid