Question

The distance of the point (a,b) from the origin is twice its distance from the point (-1,2). Find the relation between a and b

Answer 1

3a² + 3b² + 8a - 16b + 20 = 0

Step-by-step explanation:

The given points are (a, b) and (0, 0)

Then the distance between these points is

d₁ = √{(a - 0)² + (b - 0)²}

= √(a² + b²)

Again the given points are (a, b) and (- 1, 2)

Then the distance between these points is

d₂ = √{(a + 1)² + (b - 2)²}

= √(a² + b² + 2a - 4b + 5)

According to the question,

d₁ = 2 d₂

or, d₁² = 4 d₂² [ squaring on both sides ]

or, a² + b² = 4 (a² + b² + 2a - 4b + 5)

or, a² + b² = 4a² + 4b² + 8a - 16b + 20

or, 3a² + 3b² + 8a - 16b + 20 = 0

This is the required relation.