Let A be the point 1 , 2 and B be any point on the curve x 2 + y 2 = 16 . If the centre of the locus of the point P , which divides the line segment A B in the ratio 3 : 2 is the point C α , β , then the length of the line segment A C is

Step-by-step solution

Given, A be the point 1 , 2 and B be any point on the curve x 2 + y 2 = 16 , And the centre of the locus of the point P , which divides the line segment A B in the ratio 3 : 2 is the point C α , β , Now let the point on the circle x 2 + y 2 = 16 be B 4 cos θ , 4 sin θ Now using section formula in A 1 , 2 and B 4 cos θ , 4 sin θ we get, P 12 cos θ + 2 5 , 12 sin θ + 4 5 ≡ ( h , k ) ⇒ cos θ = 5 h - 2 12   &   sin θ = 5 k - 4 12 Now squaring a