Question

The eliminant after eliminating θ between the equations:
       x = a sin θ + b cos θ and y = a cos θ – b sin θ is given by

Answer 1

Answer:

x^2+y^2=a^2+b^2

Step-by-step explanation:

x=a sinθ + b cosθ;

y=acosθ-bsinθ;

Squaring the two equations we get

x^2=a^2 sin^2θ +b^2 cos^2θ +2asinθbcosθ

y^2=a^2cos^2θ-b^2sin^2θ-2acosθbsinθ

Adding the two

x^2+y^2=a^2sin^2θ+a^2cos^2θ+b^2cos^2θ-b^2sin^2θ

x^2+y^2=a^2(1)+b^2(cos^2θ+1-cos^2θ)

x^2+y^2=a^2+b^2;