The line \[x\cos \alpha +y\sin \alpha =p\] will be a tangent to the conic \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\], if [Roorkee 1978]

• A.            \[{{p}^{2}}={{a}^{2}}{{\sin }^{2}}\alpha +{{b}^{2}}{{\cos }^{2}}\alpha \]
• B.            \[{{p}^{2}}={{a}^{2}}+{{b}^{2}}\]
• C.            \[{{p}^{2}}={{b}^{2}}{{\sin }^{2}}\alpha +{{a}^{2}}{{\cos }^{2}}\alpha \]
• D.            None of these