Question

Find the coordinates of P so that AP is 1/4 of AB in with A(-5,4) and B(7,-4).

Answer 1

EXPLANATION:

Let the coordinates of P are (x, y)

Then AP = √{(x + 5)² + (y - 4)²} units

= √(x² + y² + 10x - 8y + 41) units

and AB = √{(- 5 - 7)² + (4 + 4)²} units

= √{(- 12)² + 8²} units

= √208 units

ATQ,

AP = 1/4 * AB

or, AP² = 1/16 * AB²

or, x² + y² + 10x - 8y + 41 = 1/16 * 208

or, x² + y² + 10x - 8y + 41 = 13

or, x² + y² + 10x - 8y + 28 = 0

We can conclude, x² + y² + 10x - 8y + 28 = 0 to be the locus of the point P.

Note: With the condition given, we cannot find the coordinates of P and so find the locus of the point P.