Question

A is a point on x axis and B is a point on y axis such that 2l[OA]+3l[OB] = 6, O being the origin. Find the equation of the locus from the midpoint P of segment AB

Answer 1

The locus of the mid point is

21x + 31y = 3

EXPLAINATION

Let

• Co-ordinate of A be (X, 0)
• Co-ordinate of B be (0, Y)
• Co-ordinate of mid point, P be (x,y)

Then, by section formula

$(x,y) = ( \frac{X+0}{2} , \frac{0+Y}{2} )$

$(x,y) = ( \frac{X}{2} , \frac{Y}{2} )$

$X = 2x , Y = 2y$

It is given that

21(OA) + 31(OB) = 6

⇒ 21X + 31Y = 6

⇒ 21(2x) + 31(2y) = 6

⇒ 21x + 31y = 3