A circle with centre ( 2 , 3 ) and radius 4 intersects the line x + y = 3 at the points P and Q . If the tangents at P and Q intersect at the point S ( α , β ) , then 4 α - 7 β is equal to

Step-by-step solution

A Circle having the centre 2 , 3 and radius 4 . So, the equation of circle will be x - 2 2 + y - 3 2 = 16 ⇒ x 2 + y 2 - 4 x - 6 y - 3 = 0 Now, it is given x + y = 3 passes through two points P   &   Q on circle and tangents are drawn at P   &   Q intersect at S α , β , So, x + y = 3 will be chord of contact. Now equation of chord of contact will be T α , β = 0 ⇒ α x + β y - 2 x + α - 3 y + β - 3 = 0 ⇒ x α - 2 + y β - 3 -