Find the relation obtained by eliminating `theta` from the equations `x=a cos theta+b sin theta` and `y=a sin theta- b sin theta`.

Explanation

Given, `x=a cos theta + b sin theta `
`x^(2)=(a cos theta + b sin theta )^(2)`
`=a^(2)cos^(2)theta+b^(2)sin^(2)theta+2ab cos theta sin theta `
Also `y=a sin theta - b cos theta`
`y^(2)=a^(2)sin^(2)theta+b^(2)cos^(2) theta-2 ab sin theta cos theta `
`x^(2)+y^(2)=a^(2)(sin^(2) theta + cos^(2) theta)+b^(2)(cos^(2)theta+sin^(2) theta )`
`=a^(2)+b^(2)`
Hence, the required relation is `x^(2)+y^(2)=a^(2)+b^(2)`.