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Let A ( a , 0 ) B ( 0 , b )
AB = 5
√ [ a² + b ² ] =5
[ a² + b ² ] = 25
let P〈 x , y 〉
as p divides AB in 2 : 3 externaly
A 〈 a, 0) B 〈 0, b 〉
x = [2 * 0 + 3* a ] /(2+3)
x = 3a / 5
a = 5x / 3 ........(1)
y= [2* b + 3 * 0 ] / (2+3)
y= 2b / 5
b= 5y / 2 .........(2)
Squaring and adding (1) and (2) ,
a ² + b² = ( 25 x² / 9 ) + ( 25 y² / 4 )
a ² + b ² = [ 100 x ² + 225 y ² ] / 36
25 = [ 100 x ² + 225 y ² ] / 36 {{ ∵ a² + b²= 5 }}
900 = 100 x ² + 25 y ²
Which is Required Locus of Point 'P' & it is an ELLIPSE
AB = 5
√ [ a² + b ² ] =5
[ a² + b ² ] = 25
let P〈 x , y 〉
as p divides AB in 2 : 3 externaly
A 〈 a, 0) B 〈 0, b 〉
x = [2 * 0 + 3* a ] /(2+3)
x = 3a / 5
a = 5x / 3 ........(1)
y= [2* b + 3 * 0 ] / (2+3)
y= 2b / 5
b= 5y / 2 .........(2)
Squaring and adding (1) and (2) ,
a ² + b² = ( 25 x² / 9 ) + ( 25 y² / 4 )
a ² + b ² = [ 100 x ² + 225 y ² ] / 36
25 = [ 100 x ² + 225 y ² ] / 36 {{ ∵ a² + b²= 5 }}
900 = 100 x ² + 25 y ²
Which is Required Locus of Point 'P' & it is an ELLIPSE
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