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.
Create a free account to view solution
View Solution FreeMore Circle Questions
The equation of the normal to the circle x2 + y2 = 9 at the point is -...Find the co-ordinates of a point p on line x + y = _ 13, nearest to the circle x2 + y2 + 4x + 6y _ 5 = 0...If the circles of same radius a and centres at (2, 3) and (5, 6) cut orthogonally, then a is equal to-...If a circle of constant radius 3k passes through the origin ′O′ and meets co-ordinate axes at A and B then t...For the curve 5(x - 1)2 + 5(y - 2)2 = 3(2x + y-1)2 which of the following is true -...