CircleHard
Question
The locus of a point P(α, β) moving under the condition that the line y = αx + β a tangent to the hyperbola 
= 1 is
= 1 is Options
A.an ellipse
B.a circle
C.a parabola
D.a hyperbola
Solution
Tangent to the hyperbola = 1 is
y = mx ±
Given that y = αx + β is the tangent of hyperbola
⇒ m = α and a2m2 - b2 = β2
∴ a2α2 - b2 = β2
Locus is a2x2 - y2 = b2 which is hyperbola.
= 1 is y = mx ±
Given that y = αx + β is the tangent of hyperbola
⇒ m = α and a2m2 - b2 = β2
∴ a2α2 - b2 = β2
Locus is a2x2 - y2 = b2 which is hyperbola.
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