Question

Compute, in terms of A, B, h, and k, the area enclosed by the curve defined by parametric equations. x(θ)=Acosθ+h and y(θ)=Bsinθ+k. 0≤θ≤2π.?

Answer 1

the area is just

∫[0,2π] y(t) dx/dt dt
= ∫[0,2π] (Bsint+k)(-Asint) dt
= ∫[0,2π] -ABsin^2(t) - kAsin(t) dt
= (-AB/2)(t-sint cost) + kAcost [0,2π]
= (AB/2 (2π) + kA) - (kA)
= πAB

This is true, of course, since the curves describe the ellipse

(x-h)^2/B^2 + (y-k)^2/A^2 = 1

and the area of an ellipse with semi-axes A and B is πAB

Answer 2

eweeee

Answer 3

So these set of equations give an eclipse. Area of any eclipse will be piAB where A and B are coefficients of sine and cosine. The reason why h and k donot affect the area is because the eclipse is merely shifted up or down and right or left by these values and the shape of the eclipse is unaffected.

Answer 4

Yo it's 2019 tf you answering for? @Bamboozler

Answer 5

Ur mom @Chigga Wigga

Answer 6

A little correction to Bamboozler's comment:
Since A and B can also take negative values, the total unsigned area would be: |-piAB|. The minus sign is there when calculations are done.