The locus of a point \[P(\alpha ,\,\beta )\] moving under the condition that the line \[y=\alpha x+\beta \] is a tangent to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] is [AIEEE 2005]

The locus of a point \[P(\alpha ,\,\beta )\] moving under the conditio

1.	The locus of a point \[P(\alpha ,\,\beta )\] moving under the condition that the line \[y=\alpha x+\beta \] is a tangent to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] is [AIEEE 2005]
A.	A parabola
B.	A hyperbola
C.	An ellipse
D.	A circle
Answer» C. An ellipse

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The locus of a point \[P(\alpha ,\,\beta )\] moving under the condition that the line \[y=\alpha x+\beta \] is a tangent to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] is [AIEEE 2005]

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