Question

A straight line passes through the point(3,-2). find the locus of the middle point of the portion of the line intercepted between the axes

Answer 1

I think this helps u

Answer 2

Locus of Mid-Point is 3y - 2x = 2xy

Step-by-step explanation:

Let us assume the equation of line as-

$\frac {x}{a} + \frac {y}{b} = 1$ """(1) (Variation in values of a as well as b)

Since the line (1) passes through the point (3,-2),

Therefore,

$\frac {3}{a} - \frac {2}{b} = 1$ """(2)

• The Line (1) meets the axes in points A (a,0) and  

B (0,b), then [AB] is the portion of the line intercepted between the axes.

• Let us assume M as the midpoint of [AB],  

then the coordinates of M are ($\frac {a}{2}, \frac {b}{2}$)

• For the locus M, put $\frac {a}{2} = x\ and\ \frac {b}{2} = y$

So, a = 2x and b = 2y

Substituting these values of a and b in (ii), the required equation of the locus is

$\frac {3}{2x} - \frac {2}{2y} = 1$

3y - 2x = 2xy