Question

A is a point on the X-axis and B is a point on the Y-axis such that 2.OA=3.OB The equation of a locus of the point P which divides seg AB externally in the ratio 4:3 is

Answer 1

Step-by-step explanation:





Join / Login

Question



A and B are any two points on the positive x and y−axis respectively satisfying 2(OA)+3(OB)=10. If P is the middle point of AB then the locus of P is: 

A

2x+3y=5

B

2x+3y=10

C

3x+2y=5

D

3x+2y=10

Medium

Open in App

Solution



Verified by Toppr

Correct option is A)

According to question,

P is the mid point of AB.

So, let P(x,y).

Therefore, from mid-point formulai.e.,mid point (x,y) of (x1,y1),(x2,y2) is 

x−2x1+x2,y=2y1+y2

Hence

A(2x,0) &  B(0,2y)

And, OA=2x  &  OB=2y

So,  locus of P  =>2(2x)+3(2y)=10

=>  2x+3y=5