Find the equation of the locus of a point which moves such that its di

1.	Find the equation of the locus of a point which moves such that its distance from the point (-5, 7) is twice its distance from (-3, 1).
Answer» Let A = (-5, 7) and B = (-3, 1) and P(y, b) be any point of the locus By data PA = 2PB = PA² = 4PB² ⇒ (x + 5)⁵ + (y – 7)² = 4[(x + 3)² + (y – 1)²] ⇒ x² + 10x + 25 + y² + 49 – 14y = 4(x² + 9 + 6x + y² + 1 – 2y) = 4x² + 36 + 24x + 4y²+ 4 – 8y = 3x² + 3y² + 14x + 6y – 34 = 0 which is the equation as to the locus.

Find the equation of the locus of a point which moves such that its distance from the point (-5, 7) is twice its distance from (-3, 1).

Answer»

Let A = (-5, 7) and B = (-3, 1) and P(y, b) be any point of the locus

By data PA = 2PB = PA² = 4PB² ⇒ (x + 5)⁵ + (y – 7)²

= 4[(x + 3)² + (y – 1)²]

⇒ x² + 10x + 25 + y² + 49 – 14y

= 4(x² + 9 + 6x + y² + 1 – 2y)

= 4x² + 36 + 24x + 4y²+ 4 – 8y

= 3x² + 3y² + 14x + 6y – 34 = 0

which is the equation as to the locus.