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i would like to find the area bounded by the curve

(((x^2)/(a^2))+((y^2)/(b^2)))=xy/(c^2)

i used the substitution given x=(ar)cos(theta) and y=(ar)sin(theta)

i get :

(r^2cos^2(theta)+r^2sin^2(theta))^2=xy/(c^2)

thus r^4=xy/(c^2)

substituting x=(ar)cos(theta) and y=(ar)sin(theta) on the right hand side, i get

r^4=(r^2)(ab(cos<theta>)(sin<theta>)/c^2

then r^2=ab(cos<theta>)(sin<theta>)/c^2

then i used jacobian to transform dxdy to drd(theta):

i get abr(dr)(d(theta))

then i carried out the double integral

-- --

/ /

/ / abr(dr)(d(theta))

-- --

but i get 0. please advice

(((x^2)/(a^2))+((y^2)/(b^2)))=xy/(c^2)

i used the substitution given x=(ar)cos(theta) and y=(ar)sin(theta)

i get :

(r^2cos^2(theta)+r^2sin^2(theta))^2=xy/(c^2)

thus r^4=xy/(c^2)

substituting x=(ar)cos(theta) and y=(ar)sin(theta) on the right hand side, i get

r^4=(r^2)(ab(cos<theta>)(sin<theta>)/c^2

then r^2=ab(cos<theta>)(sin<theta>)/c^2

then i used jacobian to transform dxdy to drd(theta):

i get abr(dr)(d(theta))

then i carried out the double integral

-- --

/ /

/ / abr(dr)(d(theta))

-- --

but i get 0. please advice

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