An isosceles triangle with base 24 and legs 15 each is inscribed in a circle with centre at `(-1, 1)`. The locus of the centroid of that `Delta` is

Options

A. `4(x^(2)+y^(2)) +8x - 8y - 73 = 0`
B. `2(x^(2)+y^(2)) +4x - 4y - 31 = 0`
C. `2(x^(2)+y^(2)) +4x - 4y - 21 = 0`
D. `4(x^(2)+y^(2)) +8x - 8y - 161 = 0`

Answer

D

Explanation

`(r-9)^(2) + 12^(2) = r^(2)`
`rArr 81 - 18r +144 = 0`
`rArr r = (255)/(18) = (25)/(2)`
Locus is a concentric circle with radius PG.
`PG = (r-9) +(1)/(3) (9)`
`= r - 6`
`=(25)/(2) -6 = (13)/(2)`
Lcus is `(x+1)^(2) +(y-1)^(2) = ((13)/(2))^(2)`
`rArr x^(2) + y^(2) +2x -2y -(161)/(4) =0`