Curve question

Discus: SAT/ACT Tests and Test Preparation: April 2004 Archive: Curve question
 By Kkhimji (Kkhimji) on Monday, April 12, 2004 - 08:40 am: Edit

x=acos*
y=bsin*

what is the radius of this circle?

What is area of circle?

 By Tsunashima1 (Tsunashima1) on Monday, April 12, 2004 - 01:01 pm: Edit

That's not a circle. It's an ellipse.

 By Songster87 (Songster87) on Monday, April 12, 2004 - 03:40 pm: Edit

Square x and y, divide, and add.

x^2 = a^2 * cos^2
x^2/a^2 = cos^2

y^2 = b^2 * sin^2
y^2/b^2 = sin^2

x^2/a^2 + y^2/b^2 = cos^2 + sin^2
x^2/a^2 + y^2/b^2 = 1

And like Ts..... pointed out, it's an ellipse.

 By Kkhimji (Kkhimji) on Tuesday, April 13, 2004 - 08:53 am: Edit

Ok, how would you work out the area?

 By Deepwood6 (Deepwood6) on Tuesday, April 13, 2004 - 09:31 am: Edit

integrate that beast

 By Tsunashima1 (Tsunashima1) on Tuesday, April 13, 2004 - 09:50 am: Edit

Yeah if you do int(y dx) from 0 to 2pi you get -pi*a*b. I'm just not sure how to get rid of that negative sign.

 By Tsunashima1 (Tsunashima1) on Tuesday, April 13, 2004 - 01:14 pm: Edit

Actually I just realized we have to sweep from left to right so it will be 2pi to 0, giving the correct answer of pi*a*b.