Question

hey. must the general equation of an ellipse be x''/a'' + y''/b'' = 1 or x''/a'' + y''/b'' = 2 ? so must it always be 1 ?

Answer 1

yes it is always one due to the trigonometric identity acos^2x+bsin^2x=1, where x=acosx and y=bsinx so when u plug in these for the x's and y's in your equation then we get ((acosx)/a)^2+(bsinnx)/b)^2=1, you multiply this out and you get cos^2x+sin^2x=1. this is the proof that your equation can not equation to but it always equals unity which is one!

Answer 2

The general equation of an ellipse must always have an x^2 term and a y^2 term (and no higher-order terms) on the same side of the equal sign, and they must have the same sign. (If the signs were opposite you'd have a hyperbole.)\[\frac{(x-m)^{2}}{a^{2}} + \frac{(y-n)^{2}}{b^{2}} = 1\]This is the general equation for an ellipse with center at (m, n), with a width of 2a and height of 2b. If your equation doesn't look like this, get it in to this form first before trying to use these values.

Answer 3

thanks