If the straight line \[x\cos \alpha +y\sin \alpha =p\] be a tangent to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], then [Karnataka CET 1999]

\[{{a}^{2}}{{\sin }^{2}}\alpha +{{b}^{2}}{{\cos }^{2}}\alpha ={{p}^{2}}\]

\[{{a}^{2}}{{\cos }^{2}}\alpha +{{b}^{2}}{{\sin }^{2}}\alpha ={{p}^{2}}\]

\[{{a}^{2}}{{\cos }^{2}}\alpha -{{b}^{2}}{{\sin }^{2}}\alpha ={{p}^{2}}\]

\[{{a}^{2}}{{\sin }^{2}}\alpha -{{b}^{2}}{{\cos }^{2}}\alpha ={{p}^{2}}\]

If the straight line \[x\cos \alpha +y\sin \alpha =p\] be a tangent to

1.	If the straight line \[x\cos \alpha +y\sin \alpha =p\] be a tangent to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], then [Karnataka CET 1999]
A.	\[{{a}^{2}}{{\cos }^{2}}\alpha +{{b}^{2}}{{\sin }^{2}}\alpha ={{p}^{2}}\]
B.	\[{{a}^{2}}{{\cos }^{2}}\alpha -{{b}^{2}}{{\sin }^{2}}\alpha ={{p}^{2}}\]
C.	\[{{a}^{2}}{{\sin }^{2}}\alpha +{{b}^{2}}{{\cos }^{2}}\alpha ={{p}^{2}}\]
D.	\[{{a}^{2}}{{\sin }^{2}}\alpha -{{b}^{2}}{{\cos }^{2}}\alpha ={{p}^{2}}\]
Answer» C. \[{{a}^{2}}{{\sin }^{2}}\alpha +{{b}^{2}}{{\cos }^{2}}\alpha ={{p}^{2}}\]

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If the straight line \[x\cos \alpha +y\sin \alpha =p\] be a tangent to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], then [Karnataka CET 1999]

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