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.