what is the relation between `acostheta+bsintheta=p` and `asintheta-bcostheta=q`

If acosheta+bsintheta=4 & asintheta - bcostheta= 3 then a^2+b^2

(i) Find the equation a circle passing through the point (2+3costheta,1+3sintheta) where 'theta' is a parameter. (ii) Prove that the equations x=acostheta+bsintheta and y=asintheta-bcostheta represents a circle.

Answer each question by selecting the proper alternative from those given below each question so as to make each statement true : If acostheta+bsintheta=4 and asintheta-bcostheta=3 , then a^(2)+b^(2) =…..

If asintheta+bcostheta=c , find acostheta-bsintheta=?

If the A and B have coordinates (a costheta,bsintheta)and (-asintheta,bcostheta) respectively and O is the origin then , then show that the area of DeltaOAB) is independent of theta .

The locus of the centroid of the triangle with vertices at (acostheta,asintheta) , (bsintheta-bcostheta) and (1,0) is (here, theta is a parameter)

If x=acostheta , y=bsintheta then eliminate theta .

Locus of centroid of the triangle whose vertices are (acostheta,asintheta),(bsintheta,-bcostheta) and (2,0) where theta is a parameter is

Prove that If acostheta+bsintheta=c and asintheta-bcostheta=d eliminate theta (a,b,c,d are constants)