Math Help

[Nomad]

I know we have a few math gurus on this forum and I was wondering if one of you could lend some help. I'm stuck on a problem, but I think it's the remedial math part that screwed me up. The problem is as follows.

Show that
x=acost+h, y=bsint+k; 0≤t≤2π

are parametric equations of an ellipse with center (h,k) and axes of lengths 2a and 2b.

Now, as I see it, I should just use the equation for an ellipse which is just:
http://img.photobucket.com/albums/v248/Hallock1988/Ellipse.jpg
This makes it a trigonometric verification problem when you plug in the given X and y. Since there is a pythagorean identity that says sin^2+cos^2=1 that would verify the identity and the parametric equation.

Put in the given and it cancels out the center and you arrive at:
http://img.photobucket.com/albums/v248/Hallock1988/Ellipse2.jpg

Now when the numerators of both are squared, is the term in front also squared rooted? That would cancel out the denominator leaving me with my identity since t = x = Ө or any other variable for trigonometry.

Thanks for any help.

[Thrax]

You forgot to carry the 1.

[TheBaron]

by squaring the numerators you'll get a^2 * cos^2(t) / a^2 + b^2 * sin^2(t) / b^2 = 1

a^2 / a^2 cancels as does b^2 / b^2

you're left with cost^2(t) + sin^2(t) = 1
which is a trigonometric identity

so 1 = 1, you must have an ellipse

[Nomad]

Okay, I was just checking to make sure the term in front wasn't squared some other way. Thanks.