If the chord xcosα+ysinα=p of the hyperbola x216−y218=1 subtends a right angle at the centre, and the diameter of the circle, concentric with the hyperbola to which the given chord is a tangent is d units, then the value of d4 is
Open in App
Solution
Equation of hyperbola is x216−y218=1 or9x2−8y2−144=0
Homogenizing hyperbola equation using xcosα+ysinαp=1
we get 9x2−8y2−144(xcosα+ysinαp)2=0
Since these lines are perpendicular to each other ∴9p2−8p2−144(cos2α+sin2α)=0 ⇒p2=144orp=±12 ⇒ radius=|p|√cos2α+sin2α=12 ∴radius of the circle =12 unit and, diameter of the circle(d)=24 unit ∴d4=6