`x/acostheta+y/bsintheta=1, x/asintheta-y/bcostheta=1` then `x^2/a^2+y^2/b^2=`

Options

A. `x^(2)+y^(2)=a^(2)+b^(2)`
B. `x^(2)/a^(2) +y^(2)/b^(2) =2`
C. `a^(2)x^(2)+b^(2)y^(2)=1`
D. None of the above

Answer

B

Explanation

`x/a cos theta + y/b sin theta =1, x/a sin theta - y/b cos theta =1`
Squaring and adding , we get
` (x/a cos theta + y/b sin theta)^(2) + (x/a sin theta -y/a cos theta)^(2) =1 +1`
` Rightarrow x^(2)/a^(2) + y^(2)/b^(2) =2`