Question

If \(S = \{(x,y)\;|\; x = 2\cos t + 3\sin t,\; y = 3\cos t + 2\sin t,\; t \in \mathbb{R}\}\), then the points of \(S\) lie on the curve: 

• A. \(13x^{2}+24xy+13y^{2}=25\)
• B. \(x^{2}+y^{2}+12x+12y+4=0\)
• C. \(13x^{2}-24xy+13y^{2}=25\)
• D. \(x^{2}-2xy+y^{2}=8\)

Hint:

Eliminate parameters using matrix inversion when x,y are linear in sin and cos.

Answer 1

The Correct Option is C