question_answer

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  Solved  Paper-2005

A) a hyperbola       

B)        a parabola          

C)        a circle            

D)        an ellipse

Correct Answer: A

Solution :

A lineis tangent to hyperbola if . Lineis tangent to the hyperbola if So, locus of \[(\alpha ,\,\,\beta )\,\] is Since, this equation represents a hyperbola, so focus of a pointis a hyperbola.