Question

The locus of a point which divides the join of A(-1,1)and a variable point P on the circle xsquqre+y square=4 in the ratio 3:2 is

Answer 1

x² + y² =(2)²
let (2cos∅, 2sin∅) is the point lies on circle .
according to question a unknown point ( a, b)
divide the line joining points AP is 3 : 2
use section formula,

a = { 6cos∅ -2 }/5

(5a + 2 )/6 = cos∅ ---------(1)

b = { 6sin∅ +2}/5

(5b -2)/6 = sin∅ ------------(2)

we know,

sin²∅ + cos²∅ = 1

put equations (1) and (2)

(5b-2)²/36 +(5a+2)/36 = 1

put a = x and b = y

then,
(5x + 2)² + (5y -2)² = 36

Answer 2

Answer:

answer of this question is 25(x^2+y^2) + 20( x-y) -28=0